Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
30101	Evaluate the Limit	limit as x approaches 3 of (5x^2+14x-3)/(x^2+3x)	$lim_{x \to 3} \frac{5 x^{2} + 14 x - 3}{x^{2} + 3 x}$
30102	Evaluate the Limit	limit as x approaches 3 of (5x-2)/(x-3)	$lim_{x \to 3} \frac{5 x - 2}{x - 3}$
30103	Evaluate the Limit	limit as x approaches 3 of 6/(x-3)	$lim_{x \to 3} \frac{6}{x - 3}$
30104	Evaluate the Limit	limit as x approaches 3 of (7/(1212 root of x^5))-8 cube root of x+1/( cube root of x^2)	$lim_{x \to 3} (\frac{7}{12 \sqrt[12]{x^{5}}}) - 8 \sqrt[3]{x} + \frac{1}{\sqrt[3]{x^{2}}}$
30105	Evaluate the Limit	limit as x approaches 3 of ( natural log of x-2)/(x-3)	$lim_{x \to 3} \frac{\ln (x - 2)}{x - 3}$
30106	Evaluate the Limit	limit as x approaches -3 of square root of 9-x^2	$lim_{x \to - 3} \sqrt{9 - x^{2}}$
30107	Evaluate the Limit	limit as x approaches 3 from the left of square root of (x-1)/(x-3)	$lim_{x \to 3} \sqrt{\frac{x - 1}{x - 3}}$
30108	Evaluate the Limit	limit as x approaches 3 of square root of x^2+12x+36	$lim_{x \to 3} \sqrt{x^{2} + 12 x + 36}$
30109	Evaluate the Limit	limit as x approaches 3 of square root of x^2+2x+6	$lim_{x \to 3} \sqrt{x^{2} + 2 x + 6}$
30110	Evaluate the Integral	integral of cos(2x-1) with respect to x	$\int \cos (2 x - 1) d x$
30111	Evaluate the Limit	limit as x approaches -3 of square root of 10x+99	$lim_{x \to - 3} \sqrt{10 x + 99}$
30112	Evaluate the Limit	limit as x approaches 3 of square root of 3x+5	$lim_{x \to 3} \sqrt{3 x + 5}$
30113	Evaluate the Limit	limit as x approaches 3 of square root of 3x-9	$lim_{x \to 3} \sqrt{3 x - 9}$
30114	Evaluate the Limit	limit as x approaches 3 of square root of 6x-2	$lim_{x \to 3} \sqrt{6 x - 2}$
30115	Evaluate the Integral	integral of sin(7x) with respect to x	$\int \sin (7 x) d x$
30116	Evaluate the Limit	limit as x approaches 3 of cube root of (1-x^2)/(1-x^3)	$lim_{x \to 3} \sqrt[3]{\frac{1 - x^{2}}{1 - x^{3}}}$
30117	Evaluate the Limit	limit as x approaches 3 of cube root of x^2-10	$lim_{x \to 3} \sqrt[3]{x^{2} - 10}$
30118	Evaluate the Limit	limit as x approaches 0 of (x^4)cos(2/x)	$lim_{x \to 0} (x^{4}) \cos (\frac{2}{x})$
30119	Evaluate the Limit	limit as x approaches 3 of -2/( cube root of x^2-9)	$lim_{x \to 3} - \frac{2}{\sqrt[3]{x^{2} - 9}}$
30120	Evaluate the Limit	limit as x approaches -3 from the left of 2/(x+3)	$lim_{x \to - 3} \frac{2}{x + 3}$
30121	Evaluate the Limit	limit as x approaches 3 of (27-x^3)/(x^2-5x+6)	$lim_{x \to 3} \frac{27 - x^{3}}{x^{2} - 5 x + 6}$
30122	Evaluate the Limit	limit as x approaches 3 of (2x-8)/(5x-15)	$lim_{x \to 3} \frac{2 x - 8}{5 x - 15}$
30123	Evaluate the Integral	integral of 2ydy with respect to y	$\int 2 yds y d y$
30124	Evaluate the Limit	limit as x approaches 3 of (1/(x-3))(1/( square root of x+1)-1/2)	$lim_{x \to 3} (\frac{1}{x - 3}) (\frac{1}{\sqrt{x + 1}} - \frac{1}{2})$
30125	Evaluate the Limit	limit as x approaches 3 of 1/(3-x)	$lim_{x \to 3} \frac{1}{3 - x}$
30126	Evaluate the Limit	limit as x approaches 3 of (1/(412 root of x^5)-8 cube root of x)+1/( cube root of x^2)	$lim_{x \to 3} (\frac{1}{4 \sqrt[12]{x^{5}}} - 8 \sqrt[3]{x}) + \frac{1}{\sqrt[3]{x^{2}}}$
30127	Evaluate the Limit	limit as x approaches 3 of (2x^2-7x+3)/(x^2+x-12)	$lim_{x \to 3} \frac{2 x^{2} - 7 x + 3}{x^{2} + x - 12}$
30128	Evaluate the Limit	limit as x approaches 3 from the left of 2/(x-3)	$lim_{x \to 3} \frac{2}{x - 3}$
30129	Evaluate the Limit	limit as x approaches 3 of (4x^2)/(2x^2)-(5x)/(3x)-21/9	$lim_{x \to 3} \frac{4 x^{2}}{2 x^{2}} - \frac{5 x}{3 x} - \frac{21}{9}$
30130	Evaluate the Limit	limit as a approaches -3 of (3a^2-2a-1)/(a^2+a+2)	$lim_{a \to - 3} \frac{3 a^{2} - 2 a - 1}{a^{2} + a + 2}$
30131	Evaluate the Limit	limit as x approaches 3 of (6x^2-18x)/(9-x^2)	$lim_{x \to 3} \frac{6 x^{2} - 18 x}{9 - x^{2}}$
30132	Evaluate the Limit	limit as x approaches 3 of ( square root of x+13-2* square root of x+1)/(x^2-9)	$lim_{x \to 3} \frac{\sqrt{x + 13} - 2 \cdot \sqrt{x + 1}}{x^{2} - 9}$
30133	Evaluate the Limit	limit as x approaches -3 of ( square root of 2x+22-4)/(x+3)	$lim_{x \to - 3} \frac{\sqrt{2 x + 22} - 4}{x + 3}$
30134	Evaluate the Limit	limit as x approaches 3 of ( square root of 3x+16-5)/(x-3)	$lim_{x \to 3} \frac{\sqrt{3 x + 16} - 5}{x - 3}$
30135	Evaluate the Limit	limit as x approaches 3 of ( square root of x-3)/(x-9)	$lim_{x \to 3} \frac{\sqrt{x} - 3}{x - 9}$
30136	Evaluate the Limit	limit as x approaches 3 of (x^2-3x-10)/(x-5)	$lim_{x \to 3} \frac{x^{2} - 3 x - 10}{x - 5}$
30137	Evaluate the Limit	limit as x approaches 3 from the left of (x^2-x-6)/(x-3)	$lim_{x \to 3} \frac{x^{2} - x - 6}{x - 3}$
30138	Evaluate the Limit	limit as x approaches 3 of (x^(2-9))/(x^(2-5x+6))	$lim_{x \to 3} \frac{x^{2 - 9}}{x^{2 - 5 x + 6}}$
30139	Evaluate the Limit	limit as x approaches 3 of (x^3-x^2-9x+9)/(x^4-8x^2-9)	$lim_{x \to 3} \frac{x^{3} - x^{2} - 9 x + 9}{x^{4} - 8 x^{2} - 9}$
30140	Evaluate the Limit	limit as x approaches -3 of (x^3-2x^2-11x+12)/(x+3)	$lim_{x \to - 3} \frac{x^{3} - 2 x^{2} - 11 x + 12}{x + 3}$
30141	Evaluate the Limit	limit as x approaches 3 of (x^3-3y)/(x^2-3)	$lim_{x \to 3} \frac{x^{3} - 3 y}{x^{2} - 3}$
30142	Evaluate the Limit	limit as x approaches 3 of (x^3-4x-39)/(x^3-27)	$lim_{x \to 3} \frac{x^{3} - 4 x - 39}{x^{3} - 27}$
30143	Evaluate the Limit	limit as x approaches 3 of (x^4-81)/(x^2-x-6)	$lim_{x \to 3} \frac{x^{4} - 81}{x^{2} - x - 6}$
30144	Evaluate the Limit	limit as x approaches 3 of (x-3)csc(pix)	$lim_{x \to 3} (x - 3) \csc (π x)$
30145	Evaluate the Limit	limit as x approaches 3 of x-5	$lim_{x \to 3} x - 5$
30146	Evaluate the Limit	limit as x approaches 3 of 2f(x)	$lim_{x \to 3} 2 f (x)$
30147	Evaluate the Limit	limit as x approaches 3 of 2f(x)+g(x)	$lim_{x \to 3} 2 f (x) + g (x)$
30148	Evaluate the Limit	limit as x approaches 3 of (x-3)/( square root of 7x-5-4)	$lim_{x \to 3} \frac{x - 3}{\sqrt{7 x - 5} - 4}$
30149	Evaluate the Limit	limit as x approaches 3 of ((x^2-4x)-f*2)/(x-3)	$lim_{x \to 3} \frac{(x^{2} - 4 x) - f \cdot 2}{x - 3}$
30150	Evaluate the Limit	limit as x approaches 3 of ((x^2-9x)-(36-54))/(x-3)	$lim_{x \to 3} \frac{(x^{2} - 9 x) - (36 - 54)}{x - 3}$
30151	Evaluate the Limit	limit as x approaches -3 of (x^3-4x+15)/(x^2-x-12)	$lim_{x \to - 3} \frac{x^{3} - 4 x + 15}{x^{2} - x - 12}$
30152	Evaluate the Limit	limit as x approaches -3 of 1/(x+3)	$lim_{x \to - 3} \frac{1}{x + 3}$
30153	Evaluate the Limit	limit as x approaches 3 of 1/2x-7	$lim_{x \to 3} \frac{1}{2} x - 7$
30154	Evaluate the Limit	limit as x approaches -3 of -1/3x-1	$lim_{x \to - 3} - \frac{1}{3} x - 1$
30155	Evaluate the Limit	limit as x approaches 3 of (2x^2-6x)/(x-3)	$lim_{x \to 3} \frac{2 x^{2} - 6 x}{x - 3}$
30156	Evaluate the Limit	limit as x approaches 3 of (2x^3-54)/(x^2-9)	$lim_{x \to 3} \frac{2 x^{3} - 54}{x^{2} - 9}$
30157	Evaluate the Limit	limit as x approaches 3 of (2x^3-8)/(5x+6)	$lim_{x \to 3} \frac{2 x^{3} - 8}{5 x + 6}$
30158	Evaluate the Limit	limit as x approaches 3 from the left of -2/(x-3)	$lim_{x \to 3} \frac{- 2}{x - 3}$
30159	Evaluate the Limit	limit as x approaches 3 of 2/(x-3)	$lim_{x \to 3} \frac{2}{x - 3}$
30160	Evaluate the Limit	limit as x approaches 3 of 3/4x+1	$lim_{x \to 3} \frac{3}{4} x + 1$
30161	Evaluate the Limit	limit as x approaches -3 of (5x^2+16x+3)/(x+3)	$lim_{x \to - 3} \frac{5 x^{2} + 16 x + 3}{x + 3}$
30162	Evaluate the Limit	limit as x approaches 3 of -ax^2+bx-3	$lim_{x \to 3} - a x^{2} + b x - 3$
30163	Evaluate the Limit	limit as x approaches -3 of -x^2+2x-6	$lim_{x \to - 3} - x^{2} + 2 x - 6$
30164	Evaluate the Limit	limit as x approaches 3 of -x^2+5x-9	$lim_{x \to 3} - x^{2} + 5 x - 9$
30165	Evaluate the Limit	limit as x approaches -3 of -x^2+6x-1	$lim_{x \to - 3} - x^{2} + 6 x - 1$
30166	Evaluate the Limit	limit as x approaches 3 of x^2+8x-2	$lim_{x \to 3} x^{2} + 8 x - 2$
30167	Evaluate the Limit	limit as x approaches 25 of t+5(t^(-1/2))	$lim_{x \to 25} t + 5 (t^{- \frac{1}{2}})$
30168	Evaluate the Limit	limit as x approaches 27 of (x^(1/3)-3)/(x-27)	$lim_{x \to 27} \frac{x^{\frac{1}{3}} - 3}{x - 27}$
30169	Evaluate the Limit	limit as x approaches 27 of x^(4/3)	$lim_{x \to 27} x^{\frac{4}{3}}$
30170	Evaluate the Limit	limit as x approaches 2pi of (sin(x))/(cos(x))	$lim_{x \to 2 π} \frac{\sin (x)}{\cos (x)}$
30171	Evaluate the Limit	limit as x approaches -2pi of square root of x+11cos(x+2pi)	$lim_{x \to - 2 π} \sqrt{x + 11} \cos (x + 2 π)$
30172	Evaluate the Limit	limit as x approaches -2pi of square root of x+15cos(x+2pi)	$lim_{x \to - 2 π} \sqrt{x + 15} \cos (x + 2 π)$
30173	Evaluate the Limit	limit as x approaches -2R of (2x+3)/(x+2)	$lim_{x \to - 2 R} \frac{2 x + 3}{x + 2}$
30174	Evaluate the Limit	limit as x approaches 3 of (x-3)(x-4)	$lim_{x \to 3} (x - 3) (x - 4)$
30175	Evaluate the Limit	limit as x approaches 3 of ((5/x)-(5/3))/(x-3)	$lim_{x \to 3} \frac{(\frac{5}{x}) - (\frac{5}{3})}{x - 3}$
30176	Evaluate the Limit	limit as x approaches -3 of (t^2-9)/(2t^2+7t+3)	$lim_{x \to - 3} \frac{t^{2} - 9}{2 t^{2} + 7 t + 3}$
30177	Evaluate the Limit	limit as x approaches 3 of ((3)^2+3-12)/(3-3)	$lim_{x \to 3} \frac{{(3)}^{2} + 3 - 12}{3 - 3}$
30178	Evaluate the Limit	limit as x approaches -3 of ( square root of 25+x-5)/x	$lim_{x \to - 3} \frac{\sqrt{25 + x} - 5}{x}$
30179	Evaluate the Limit	limit as x approaches 3 of ( square root of x+1-2)/(x^3-8x-3)	$lim_{x \to 3} \frac{\sqrt{x + 1} - 2}{x^{3} - 8 x - 3}$
30180	Evaluate the Limit	limit as x approaches 3 of (-x^2-2x-15)/(x+3)	$lim_{x \to 3} \frac{- x^{2} - 2 x - 15}{x + 3}$
30181	Evaluate the Limit	limit as x approaches 3 of (x^2*(7x)+12)/(x^2-9)	$lim_{x \to 3} \frac{x^{2} \cdot (7 x) + 12}{x^{2} - 9}$
30182	Evaluate the Limit	limit as x approaches -3 of (x^2-9)/(4x^2-11x-3)	$lim_{x \to - 3} \frac{x^{2} - 9}{4 x^{2} - 11 x - 3}$
30183	Evaluate the Limit	limit as x approaches 3 of (x^2-9)/(x-3)-((x^2-1)/(x+1))	$lim_{x \to 3} \frac{x^{2} - 9}{x - 3} - (\frac{x^{2} - 1}{x + 1})$
30184	Evaluate the Limit	limit as x approaches 3 of (x^2-x-6)/(x^2-9)	$lim_{x \to 3} \frac{x^{2} - x - 6}{x^{2} - 9}$
30185	Evaluate the Limit	limit as x approaches 3 of 3x-1	$lim_{x \to 3} 3 x - 1$
30186	Evaluate the Limit	limit as x approaches 3 of 4t^2-2t+1	$lim_{x \to 3} 4 t^{2} - 2 t + 1$
30187	Evaluate the Limit	limit as x approaches 3 of 4x+1	$lim_{x \to 3} 4 x + 1$
30188	Evaluate the Limit	limit as x approaches 3 of 5x^2+6x+2x^3-10	$lim_{x \to 3} 5 x^{2} + 6 x + 2 x^{3} - 10$
30189	Evaluate the Limit	limit as x approaches -3 of 6-3x3/(5x^-4)	$lim_{x \to - 3} 6 - 3 x \frac{3}{5 x^{- 4}}$
30190	Evaluate the Limit	limit as x approaches 3 of 6-x	$lim_{x \to 3} 6 - x$
30191	Evaluate the Limit	limit as x approaches -3 of 7x+2	$lim_{x \to - 3} 7 x + 2$
30192	Evaluate the Limit	limit as x approaches 3 of 7x-4	$lim_{x \to 3} 7 x - 4$
30193	Evaluate the Limit	limit as x approaches 3 from the left of f(x)	$lim_{x \to 3} f (x)$
30194	Evaluate the Limit	limit as x approaches 3 of x^2-4x+10	$lim_{x \to 3} x^{2} - 4 x + 10$
30195	Evaluate the Limit	limit as x approaches 3 from the left of (x+4)/(x-2)	$lim_{x \to 3} \frac{x + 4}{x - 2}$
30196	Solve for x	natural log of x- natural log of x^2+ natural log of 2=0	$\ln (x) - \ln (x^{2}) + \ln (2) = 0$
30197	Evaluate the Limit	limit as x approaches -3 of 2x^3+3x-5	$lim_{x \to - 3} 2 x^{3} + 3 x - 5$
30198	Evaluate the Limit	limit as x approaches 3 of (2x^3+6x^2+x-3)x-3	$lim_{x \to 3} (2 x^{3} + 6 x^{2} + x - 3) x - 3$
30199	Evaluate the Limit	limit as x approaches 3 of 2x^3-5x^2+4	$lim_{x \to 3} 2 x^{3} - 5 x^{2} + 4$
30200	Evaluate the Limit	limit as x approaches -3 of (3x^2+2x-1)/(x^2+3x-2)	$lim_{x \to - 3} \frac{3 x^{2} + 2 x - 1}{x^{2} + 3 x - 2}$