Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
48101	Find the Tangent Line at x=1	f(x)=(6x-5)^(1/2) , x=1	$f (x) = {(6 x - 5)}^{\frac{1}{2}}$ , $x = 1$
48102	Find the Critical Points	(x+2)^(4/7)	${(x + 2)}^{\frac{4}{7}}$
48103	Find the Critical Points	square root of x natural log of 6x	$\sqrt{x} \ln (6 x)$
48104	Find the Critical Points	cube root of x+3	$\sqrt[3]{x + 3}$
48105	Find the Critical Points	19x^4-114x^2	$19 x^{4} - 114 x^{2}$
48106	Find the Critical Points	20-20000000/(x^2)	$20 - \frac{20000000}{x^{2}}$
48107	Find the Critical Points	2cos(theta)+sin(theta)^2	$2 \cos (θ) + \sin^{2} (θ)$
48108	Find the Critical Points	2cos(4x)+4x	$2 \cos (4 x) + 4 x$
48109	Find the Critical Points	20000000/x+20x	$\frac{20000000}{x} + 20 x$
48110	Find the Critical Points	1/2x^4-x^3-18x^2-3	$\frac{1}{2} x^{4} - x^{3} - 18 x^{2} - 3$
48111	Find the Critical Points	-4x^2+48x	$- 4 x^{2} + 48 x$
48112	Find the Critical Points	x^3-7x^2-24x+5	$x^{3} - 7 x^{2} - 24 x + 5$
48113	Find the Critical Points	x^3-27x+8	$x^{3} - 27 x + 8$
48114	Find the Critical Points	x^3+12x^2-27x	$x^{3} + 12 x^{2} - 27 x$
48115	Find the Critical Points	x^(2/3)-4	$x^{\frac{2}{3}} - 4$
48116	Find the Critical Points	(4x)/(x^2+25)	$\frac{4 x}{x^{2} + 25}$
48117	Find the Critical Points	6/(x^2+3)	$\frac{6}{x^{2} + 3}$
48118	Find the Critical Points	x^4e^(-5x)	$x^{4} e^{- 5 x}$
48119	Find the Critical Points	x^6(x-1)^5	$x^{6} {(x - 1)}^{5}$
48120	Find the Critical Points	x^6e^(-7x)	$x^{6} e^{- 7 x}$
48121	Find the Critical Points	45x^2-492x-2466	$45 x^{2} - 492 x - 2466$
48122	Find the Critical Points	xe^(-7x)	$x e^{- 7 x}$
48123	Find the Critical Points	2x^3+3x^2-36x+5	$2 x^{3} + 3 x^{2} - 36 x + 5$
48124	Find the Critical Points	x^3-3x+9	$x^{3} - 3 x + 9$
48125	Find the Critical Points	x^3+9x^2-48x	$x^{3} + 9 x^{2} - 48 x$
48126	Find the Critical Points	5x-4 natural log of x	$5 x - 4 \ln (x)$
48127	Find the Critical Points	3x^3+9x^2-72x	$3 x^{3} + 9 x^{2} - 72 x$
48128	Find the Critical Points	3x^3-4x^4	$3 x^{3} - 4 x^{4}$
48129	Find the Critical Points	4theta-tan(theta)	$4 θ - \tan (θ)$
48130	Find the Critical Points	48x-8x^2	$48 x - 8 x^{2}$
48131	Find the Critical Points	-5(x^2-24x+80)^(4/5)	$- 5 {(x^{2} - 24 x + 80)}^{\frac{4}{5}}$
48132	Find the Critical Points	4x^3-12x^2+8x	$4 x^{3} - 12 x^{2} + 8 x$
48133	Find the Critical Points	x^(12/13)-x^(25/13)	$x^{\frac{12}{13}} - x^{\frac{25}{13}}$
48134	Find the Critical Points	x^(5/3)-3x^(2/3)	$x^{\frac{5}{3}} - 3 x^{\frac{2}{3}}$
48135	Find the Critical Points	e^(-1.5x^2)	$e^{- 1.5 x^{2}}$
48136	Find the Critical Points	cos(pix)	$\cos (π x)$
48137	Find the Critical Points	-e^x(x-7)	$- e^{x} (x - 7)$
48138	Find the Critical Points	-8x^3+24x+7	$- 8 x^{3} + 24 x + 7$
48139	Evaluate the Summation	sum from i=1 to 6 of 5i	$\sum_{i = 1}^{6} 5 i$
48140	Evaluate the Summation	sum from x=3 to 4 of (-21x)/5	$\sum_{x = 3}^{4} \frac{- 21 x}{5}$
48141	Evaluate the Summation	sum from x=0 to infinity of 5(3/4)^x	$\sum_{x = 0}^{\infty} 5 {(\frac{3}{4})}^{x}$
48142	Find the x and y Intercepts	r(x)=(x-5)/(x+8)	$r (x) = \frac{x - 5}{x + 8}$
48143	Find the x and y Intercepts	f(x)=(4x-1)/x	$f (x) = \frac{4 x - 1}{x}$
48144	Find the Value Using the Unit Circle	(4pi)/3	$\frac{4 π}{3}$
48145	Find the Value Using the Unit Circle	(17pi)/6	$\frac{17 π}{6}$
48146	Find the Value Using the Unit Circle	-(5pi)/3	$- \frac{5 π}{3}$
48147	Convert to Set Notation	x^2-7x-18<0	$x^{2} - 7 x - 18 < 0$
48148	Find the Value Using the Unit Circle	270 degrees	$270 °$
48149	Find the x and y Intercepts	f(x)=9x^2-11x-4	$f (x) = 9 x^{2} - 11 x - 4$
48150	Find the x and y Intercepts	f(x)=-6x+12	$f (x) = - 6 x + 12$
48151	Find the x and y Intercepts	f(x)=x^2(x-5)^3(x+3)	$f (x) = x^{2} {(x - 5)}^{3} (x + 3)$
48152	Find the x and y Intercepts	f(x)=x^3-14x^2+49x	$f (x) = x^{3} - 14 x^{2} + 49 x$
48153	Evaluate the Summation	sum from k=2 to 6 of 2^(k-1)	$\sum_{k = 2}^{6} 2^{k - 1}$
48154	Evaluate the Summation	sum from n=1 to 4 of 5-8n	$\sum_{n = 1}^{4} 5 - 8 n$
48155	Evaluate the Summation	sum from k=1 to 30 of (2/15k+1)2/15	$\sum_{k = 1}^{30} (\frac{2}{15} k + 1) \frac{2}{15}$
48156	Evaluate the Summation	sum from i=1 to 12 of 7	$\sum_{i = 1}^{12} 7$
48157	Evaluate the Summation	sum from i=1 to 21 of 3i^2+3	$\sum_{i = 1}^{21} 3 i^{2} + 3$
48158	Evaluate the Summation	sum from n=1 to 10 of 5+2(n-1)	$\sum_{n = 1}^{10} 5 + 2 (n - 1)$
48159	Evaluate the Summation	sum from i=1 to 39 of -4.1+0.4i	$\sum_{i = 1}^{39} - 4.1 + 0.4 i$
48160	Evaluate the Summation	sum from 3 to 12 of 20(0.5)^(n-1)	$\sum_{3}^{12} 20 {(0.5)}^{n - 1}$
48161	Evaluate the Summation	sum from n=1 to 8 of 2^(n-1)	$\sum_{n = 1}^{8} 2^{n - 1}$
48162	Evaluate the Summation	1.4 sum from k=1 to 10 of 49-(-7+1.4k)^2	$1.4 \sum_{k = 1}^{10} 49 - {(- 7 + 1.4 k)}^{2}$
48163	Evaluate the Summation	sum from n=1 to 35 of n	$\sum_{n = 1}^{35} n$
48164	Evaluate the Summation	sum from n=0 to infinity of (e/pi)^n	$\sum_{n = 0}^{\infty} {(\frac{e}{π})}^{n}$
48165	Evaluate the Summation	sum from n=0 to 3 of (-1/2)^n*(4)	$\sum_{n = 0}^{3} {(- \frac{1}{2})}^{n} \cdot (4)$
48166	Evaluate the Summation	sum from n=1 to 60 of 2n-7	$\sum_{n = 1}^{60} 2 n - 7$
48167	Evaluate the Summation	sum from i=1 to 25 of (i+1)/625	$\sum_{i = 1}^{25} \frac{i + 1}{625}$
48168	Evaluate the Summation	sum from i=1 to 6 of 1+(-1)^i	$\sum_{i = 1}^{6} 1 + {(- 1)}^{i}$
48169	Evaluate the Summation	sum from k=1 to 2 of (12k)/(k+2)	$\sum_{k = 1}^{2} \frac{12 k}{k + 2}$
48170	Evaluate the Summation	sum from n=1 to 90 of 3n-9	$\sum_{n = 1}^{90} 3 n - 9$
48171	Evaluate the Summation	sum from t=1 to 18 of 3t-4	$\sum_{t = 1}^{18} 3 t - 4$
48172	Evaluate the Summation	sum from n=1 to 6 of (1/5)^(n-1)	$\sum_{n = 1}^{6} {(\frac{1}{5})}^{n - 1}$
48173	Find the Inverse	f^-1(8)	$f^{- 1} (8)$
48174	Find the Inverse	square root of x-6	$\sqrt{x - 6}$
48175	Find the Absolute Max and Min over the Interval	f(x)=9+4x-4x^2 ; [0,5]	$f (x) = 9 + 4 x - 4 x^{2}$ ; $[0, 5]$
48176	Find the Absolute Max and Min over the Interval	f(x)=4x^3-4x^2-4x+8 ; [-1,2]	$f (x) = 4 x^{3} - 4 x^{2} - 4 x + 8$ ; $[- 1, 2]$
48177	Find the Absolute Max and Min over the Interval	f(x)=x/(x^2-x+4) , [0,6]	$f (x) = \frac{x}{x^{2} - x + 4}$ , $[0, 6]$
48178	Find the Absolute Max and Min over the Interval	h(t)=t/(t-2) , [3,5]	$h (t) = \frac{t}{t - 2}$ , $[3, 5]$
48179	Find the Absolute Max and Min over the Interval	f(x)=x^2-4x-9 , [0,2]	$f (x) = x^{2} - 4 x - 9$ , $[0, 2]$
48180	Find the Absolute Max and Min over the Interval	f(x)=x square root of 9-x^2 ; [-3,3]	$f (x) = x \sqrt{9 - x^{2}}$ ; $[- 3, 3]$
48181	Find the Absolute Max and Min over the Interval	t(t)=-0.3t^2+2.4t+98.3 , 0<=t<=8	$t (t) = - 0.3 t^{2} + 2.4 t + 98.3$ , $0 \leq t \leq 8$
48182	Convert to Polar Coordinates	(-7/2,(7 square root of 3)/2)	$(- \frac{7}{2}, \frac{7 \sqrt{3}}{2})$
48183	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of x^2e^(cos(1/x))	$lim_{x \to 0} x^{2} e^{\cos (\frac{1}{x})}$
48184	Evaluate Using the Squeeze Theorem	limit as x approaches 0 of xcos(1/x)	$lim_{x \to 0} x \cos (\frac{1}{x})$
48185	Evaluate Using the Squeeze Theorem	limit as x approaches negative infinity of x+ square root of x^2+2x	$lim_{x \to - \infty} x + \sqrt{x^{2} + 2 x}$
48186	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of x^(1/x)	$lim_{x \to \infty} x^{\frac{1}{x}}$
48187	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of xsin(1/x)	$lim_{x \to \infty} x \sin (\frac{1}{x})$
48188	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of (cos(2x)^2)/(x-2x)	$lim_{x \to \infty} \frac{\cos^{2} (2 x)}{x - 2 x}$
48189	Evaluate Using the Squeeze Theorem	limit as x approaches negative infinity of 2x+ square root of 4x^2+3x-2	$lim_{x \to - \infty} 2 x + \sqrt{4 x^{2} + 3 x - 2}$
48190	Find the Derivative Using Product Rule - d/dx	d/(dx)(uv)	$\frac{d}{d x} (u v)$
48191	Find the Derivative Using Product Rule - d/dx	y=(5+3x^-2)(4x^5+6x^3+10)	$y = (5 + 3 x^{- 2}) (4 x^{5} + 6 x^{3} + 10)$
48192	Find the Derivative Using Product Rule - d/dx	y=(7 square root of x+4)x^2	$y = (7 \sqrt{x} + 4) x^{2}$
48193	Find the Derivative Using Product Rule - d/dz	z=(3x+1)^4(5x-2)^3	$z = {(3 x + 1)}^{4} {(5 x - 2)}^{3}$
48194	Find the Derivative Using Product Rule - d/ds	(s^(-1/2)+2s)(7-s^-1)	$(s^{- \frac{1}{2}} + 2 s) (7 - s^{- 1})$
48195	Find the Derivative Using Product Rule - d/du	d/(dx)(uv)	$\frac{d}{d x} (u v)$
48196	Find the Derivative Using Product Rule - d/dv	d/(dx)(uv)	$\frac{d}{d x} (u v)$
48197	Find the Derivative Using Product Rule - d/d@VAR	f(x)=(5x+6)^2	$f (x) = {(5 x + 6)}^{2}$
48198	Find the Derivative Using Product Rule - d/d@VAR	h(z)=(7-z^2)(z^3-2z+3)	$h (z) = (7 - z^{2}) (z^{3} - 2 z + 3)$
48199	Find the Domain and Range	cube root of x-4	$\sqrt[3]{x - 4}$
48200	Find the Domain and Range	log base 2 of x-2	$\log_{2} (x - 2)$