Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
20701	Evaluate the Limit	limit as x approaches 1 of (x^2+6x-7)/(x^2-1)	$lim_{x \to 1} \frac{x^{2} + 6 x - 7}{x^{2} - 1}$
20702	Evaluate the Limit	limit as x approaches 1 of (x^2+x-2)/(x-3)	$lim_{x \to 1} \frac{x^{2} + x - 2}{x - 3}$
20703	Evaluate the Limit	limit as x approaches 1 of (x^2-6x+5)/(x-1)	$lim_{x \to 1} \frac{x^{2} - 6 x + 5}{x - 1}$
20704	Evaluate the Limit	limit as x approaches 1 of (x^2-5x+6)/(x-1)	$lim_{x \to 1} \frac{x^{2} - 5 x + 6}{x - 1}$
20705	Evaluate the Limit	limit as x approaches infinity of (x^5)/(5^x)	$lim_{x \to \infty} \frac{x^{5}}{5^{x}}$
20706	Evaluate the Limit	limit as x approaches 1 of (1-x)/( natural log of x)	$lim_{x \to 1} \frac{1 - x}{\ln (x)}$
20707	Evaluate the Limit	limit as x approaches 1 of (1-x+ natural log of x)/(1+cos(3pix))	$lim_{x \to 1} \frac{1 - x + \ln (x)}{1 + \cos (3 π x)}$
20708	Evaluate the Limit	limit as x approaches 1 of (1-x+ natural log of x)/(1+cos(5pix))	$lim_{x \to 1} \frac{1 - x + \ln (x)}{1 + \cos (5 π x)}$
20709	Evaluate the Limit	limit as x approaches 1 of (x^a-1)/(x^b-1)	$lim_{x \to 1} \frac{x^{a} - 1}{x^{b} - 1}$
20710	Evaluate the Limit	limit as x approaches 1 of (x^3-1)/(4x^3-x-3)	$lim_{x \to 1} \frac{x^{3} - 1}{4 x^{3} - x - 3}$
20711	Evaluate the Limit	limit as x approaches 1 of (x^(3a)-3ax+3a-1)/((x-1)^2)	$lim_{x \to 1} \frac{x^{3 a} - 3 a x + 3 a - 1}{{(x - 1)}^{2}}$
20712	Evaluate the Limit	limit as x approaches -1 of 3x^4-2x^3+4x	$lim_{x \to - 1} 3 x^{4} - 2 x^{3} + 4 x$
20713	Evaluate the Limit	limit as x approaches 1 of 2x^3-3x^2+4x+5	$lim_{x \to 1} 2 x^{3} - 3 x^{2} + 4 x + 5$
20714	Evaluate the Limit	limit as x approaches 1 of 3x-4	$lim_{x \to 1} 3 x - 4$
20715	Evaluate the Limit	limit as t approaches 0 of 3/t-3/(t^2+t)	$lim_{t \to 0} \frac{3}{t} - \frac{3}{t^{2} + t}$
20716	Evaluate the Limit	limit as x approaches 1 of xsec(x)^2-tan(x)^2-1	$lim_{x \to 1} x \sec^{2} (x) - \tan^{2} (x) - 1$
20717	Evaluate the Limit	limit as x approaches infinity of (2x^2-1)/(x^3+x^2+1)	$lim_{x \to \infty} \frac{2 x^{2} - 1}{x^{3} + x^{2} + 1}$
20718	Evaluate the Limit	limit as x approaches -1 of -x^2+9x-3	$lim_{x \to - 1} - x^{2} + 9 x - 3$
20719	Evaluate the Limit	limit as x approaches 1 of 1/(x-1)-1/( natural log of x)	$lim_{x \to 1} \frac{1}{x - 1} - \frac{1}{\ln (x)}$
20720	Evaluate the Limit	limit as x approaches infinity of e^(-3x)cos(x)	$lim_{x \to \infty} e^{- 3 x} \cos (x)$
20721	Evaluate the Limit	limit as x approaches 1 of (7x)/(x-1)-7/( natural log of x)	$lim_{x \to 1} \frac{7 x}{x - 1} - \frac{7}{\ln (x)}$
20722	Evaluate the Limit	limit as x approaches 1 of (1/( natural log of x))-(1/(x-1))	$lim_{x \to 1} (\frac{1}{\ln (x)}) - (\frac{1}{x - 1})$
20723	Evaluate the Limit	limit as x approaches 1 of 1/(e^(x-1)-1)-1/(x-1)	$lim_{x \to 1} \frac{1}{e^{x - 1} - 1} - \frac{1}{x - 1}$
20724	Evaluate the Summation	sum from n=1 to infinity of (-1/3)^(n-1)	$\sum_{n = 1}^{\infty} {(- \frac{1}{3})}^{n - 1}$
20725	Evaluate the Limit	limit as x approaches 0 of xcsc(3x)	$lim_{x \to 0} x \csc (3 x)$
20726	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(x^2+3x+2)	$lim_{x \to - 1} \frac{x^{2} - 1}{x^{2} + 3 x + 2}$
20727	Evaluate the Limit	limit as x approaches 2 of (x^4-3x^2-4)/(x-2)	$lim_{x \to 2} \frac{x^{4} - 3 x^{2} - 4}{x - 2}$
20728	Evaluate the Limit	limit as h approaches 0 of ((-9+h)^2-81)/h	$lim_{h \to 0} \frac{{(- 9 + h)}^{2} - 81}{h}$
20729	Evaluate the Limit	limit as x approaches 2 of (2x^2-9x+10)/(x-2)	$lim_{x \to 2} \frac{2 x^{2} - 9 x + 10}{x - 2}$
20730	Evaluate the Limit	limit as x approaches 2 of cos((pix)/3)	$lim_{x \to 2} \cos (\frac{π x}{3})$
20731	Evaluate the Limit	limit as x approaches infinity of 7cos(x)	$lim_{x \to \infty} 7 \cos (x)$
20732	Evaluate the Limit	limit as x approaches 0 of (tan(2x))/(sin(x))	$lim_{x \to 0} \frac{\tan (2 x)}{\sin (x)}$
20733	Evaluate the Limit	limit as x approaches -1 of g(x)	$lim_{x \to - 1} g (x)$
20734	Evaluate the Limit	limit as x approaches 1 of natural log of x/(e^(2x))	$lim_{x \to 1} \ln (\frac{x}{e^{2 x}})$
20735	Evaluate the Limit	limit as x approaches 1 of y	$lim_{x \to 1} y$
20736	Evaluate the Limit	limit as x approaches 10 of square root of 100-x^2	$lim_{x \to 10} \sqrt{100 - x^{2}}$
20737	Evaluate the Limit	limit as x approaches 10 of (x-10)/(\|x-10\|)	$lim_{x \to 10} \frac{x - 10}{\| x - 10 \|}$
20738	Evaluate the Limit	limit as x approaches -10 of f(x)	$lim_{x \to - 10} f (x)$
20739	Evaluate the Limit	limit as x approaches 1000 of x^(7/3)	$lim_{x \to 1000} x^{\frac{7}{3}}$
20740	Evaluate the Limit	limit as x approaches 10 of 1/((x-10)^2)	$lim_{x \to 10} \frac{1}{{(x - 10)}^{2}}$
20741	Evaluate the Limit	limit as x approaches 6 of ( square root of x+3-3)/(x-6)	$lim_{x \to 6} \frac{\sqrt{x + 3} - 3}{x - 6}$
20742	Evaluate the Limit	limit as x approaches -5 of (x^2-25)/(2x^2+11x+5)	$lim_{x \to - 5} \frac{x^{2} - 25}{2 x^{2} + 11 x + 5}$
20743	Evaluate the Limit	limit as x approaches 10 of ( square root of x+6-4)/(x-10)	$lim_{x \to 10} \frac{\sqrt{x + 6} - 4}{x - 10}$
20744	Evaluate the Limit	limit as x approaches 11 of (x^2-121)/(11-x)	$lim_{x \to 11} \frac{x^{2} - 121}{11 - x}$
20745	Evaluate the Limit	limit as x approaches 11 of 1/16	$lim_{x \to 11} \frac{1}{16}$
20746	Evaluate the Limit	limit as x approaches -12 of (x^2-144)/(x+12)	$lim_{x \to - 12} \frac{x^{2} - 144}{x + 12}$
20747	Evaluate the Limit	limit as x approaches 107 of (x-107)/( square root of x+14-11)	$lim_{x \to 107} \frac{x - 107}{\sqrt{x + 14} - 11}$
20748	Evaluate the Limit	limit as x approaches 12 of 6	$lim_{x \to 12} 6$
20749	Evaluate the Limit	limit as x approaches 13 of (sin(x-13))/(x^2-169)	$lim_{x \to 13} \frac{\sin (x - 13)}{x^{2} - 169}$
20750	Evaluate the Limit	limit as x approaches 4 of square root of 16-x^2	$lim_{x \to 4} \sqrt{16 - x^{2}}$
20751	Evaluate the Limit	limit as x approaches -15 of (14- square root of x^2-29)/(x+15)	$lim_{x \to - 15} \frac{14 - \sqrt{x^{2} - 29}}{x + 15}$
20752	Evaluate the Limit	limit as x approaches 15 of square root of x^2-225	$lim_{x \to 15} \sqrt{x^{2} - 225}$
20753	Evaluate the Limit	limit as x approaches 14 of square root of 3	$lim_{x \to 14} \sqrt{3}$
20754	Evaluate the Limit	limit as x approaches 3 of (x^2-9)/(x^2+2x-3)	$lim_{x \to 3} \frac{x^{2} - 9}{x^{2} + 2 x - 3}$
20755	Evaluate the Limit	limit as x approaches 1 of ( natural log of x)/(1-x)	$lim_{x \to 1} \frac{\ln (x)}{1 - x}$
20756	Evaluate the Limit	limit as x approaches 1 of square root of (8x+1)/(x+3)	$lim_{x \to 1} \sqrt{\frac{8 x + 1}{x + 3}}$
20757	Evaluate the Limit	limit as x approaches -1 of square root of u^2x^2+2xu+1	$lim_{x \to - 1} \sqrt{u^{2} x^{2} + 2 x u + 1}$
20758	Evaluate the Limit	limit as x approaches 1 of square root of 8x-3	$lim_{x \to 1} \sqrt{8 x - 3}$
20759	Evaluate the Limit	limit as x approaches -1 of square root of 6-3x	$lim_{x \to - 1} \sqrt{6 - 3 x}$
20760	Evaluate the Limit	limit as x approaches 1 of square root of 5x+4	$lim_{x \to 1} \sqrt{5 x + 4}$
20761	Evaluate the Limit	limit as x approaches -1 of x/(x^2-1)	$lim_{x \to - 1} \frac{x}{x^{2} - 1}$
20762	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(3x)+(2x)/(tan(4x))	$lim_{x \to 0} \frac{\sin (x)}{3 x} + \frac{2 x}{\tan (4 x)}$
20763	Evaluate the Limit	limit as x approaches -1 of e^(1/x)	$lim_{x \to - 1} e^{\frac{1}{x}}$
20764	Evaluate the Limit	limit as x approaches 1 of ( natural log of x^2)/(x^2-1)	$lim_{x \to 1} \frac{\ln (x^{2})}{x^{2} - 1}$
20765	Evaluate the Limit	limit as x approaches 1 of ( natural log of 2x-1)/(x-1)	$lim_{x \to 1} \frac{\ln (2 x - 1)}{x - 1}$
20766	Evaluate the Limit	limit as x approaches 1 of e^(6x^2-6x)	$lim_{x \to 1} e^{6 x^{2} - 6 x}$
20767	Evaluate the Limit	limit as x approaches 1 of (6x^4-6)/(2x-2)	$lim_{x \to 1} \frac{6 x^{4} - 6}{2 x - 2}$
20768	Evaluate the Limit	limit as x approaches 1 of 5-x	$lim_{x \to 1} 5 - x$
20769	Evaluate the Limit	limit as x approaches 1 of 9	$lim_{x \to 1} 9$
20770	Evaluate the Limit	limit as x approaches 1 of f(0.9)	$lim_{x \to 1} f (0.9)$
20771	Evaluate the Limit	limit as x approaches -1 of x/(x+1)	$lim_{x \to - 1} \frac{x}{x + 1}$
20772	Evaluate the Integral	integral from 0 to infinity of e^(-2x) with respect to x	$\int_{0}^{\infty} e^{- 2 x} d x$
20773	Evaluate the Limit	limit as t approaches 0 of 4/t-4/(t^2+t)	$lim_{t \to 0} \frac{4}{t} - \frac{4}{t^{2} + t}$
20774	Evaluate the Limit	limit as x approaches 0 of 3(1-cos(x))	$lim_{x \to 0} 3 (1 - \cos (x))$
20775	Evaluate the Limit	limit as x approaches 0 of 4sin(x-3)	$lim_{x \to 0} 4 \sin (x - 3)$
20776	Evaluate the Limit	limit as x approaches 0 of (4(sin(x)))/x	$lim_{x \to 0} \frac{4 (\sin (x))}{x}$
20777	Evaluate the Limit	limit as x approaches 0 of (3x)sin(1/x)	$lim_{x \to 0} (3 x) \sin (\frac{1}{x})$
20778	Evaluate the Limit	limit as x approaches 0 of 4	$lim_{x \to 0} 4$
20779	Evaluate the Limit	limit as x approaches 0 of 9x-8	$lim_{x \to 0} 9 x - 8$
20780	Evaluate the Limit	limit as x approaches 0 of 5x^3-7x^2+2^x-2	$lim_{x \to 0} 5 x^{3} - 7 x^{2} + 2^{x} - 2$
20781	Evaluate the Limit	limit as x approaches 0 of 7	$lim_{x \to 0} 7$
20782	Evaluate the Limit	limit as x approaches 0 of (7)+2x	$lim_{x \to 0} (7) + 2 x$
20783	Evaluate the Limit	limit as x approaches 0 of natural log of 0	$lim_{x \to 0} \ln (0)$
20784	Evaluate the Limit	limit as x approaches 0 of cot(5x)sin(10x)	$lim_{x \to 0} \cot (5 x) \sin (10 x)$
20785	Evaluate the Limit	limit as x approaches 0 of cot(2x)sin(6x)	$lim_{x \to 0} \cot (2 x) \sin (6 x)$
20786	Evaluate the Limit	limit as x approaches 0 of cos(7x)	$lim_{x \to 0} \cos (7 x)$
20787	Evaluate the Limit	limit as x approaches 0 of cos(2x)	$lim_{x \to 0} \cos (2 x)$
20788	Evaluate the Limit	limit as x approaches 0 of (cot(x))-1/x	$lim_{x \to 0} (\cot (x)) - \frac{1}{x}$
20789	Evaluate the Limit	limit as x approaches 0 of (Dx)(5 square root of 32.4x^3)	$lim_{x \to 0} (D x) (5 \sqrt{32.4 x^{3}})$
20790	Evaluate the Limit	limit as x approaches 0 of (x+sin(2x))/(x-sin(2x))	$lim_{x \to 0} \frac{x + \sin (2 x)}{x - \sin (2 x)}$
20791	Evaluate the Limit	limit as x approaches 0 of 1+csc(x)	$lim_{x \to 0} 1 + \csc (x)$
20792	Evaluate the Limit	limit as x approaches 9 of (x-9)/( square root of x-3)	$lim_{x \to 9} \frac{(x - 9)}{\sqrt{x} - 3}$
20793	Evaluate the Limit	limit as x approaches infinity of (x^3-2x+3)/(5-2x^2)	$lim_{x \to \infty} \frac{x^{3} - 2 x + 3}{5 - 2 x^{2}}$
20794	Evaluate the Limit	limit as x approaches 0 of 1-(cos(x))/(sin(x))	$lim_{x \to 0} 1 - \frac{\cos (x)}{\sin (x)}$
20795	Evaluate the Limit	limit as x approaches pi of 9cot(x)	$lim_{x \to π} 9 \cot (x)$
20796	Evaluate the Limit	limit as x approaches -1 of (5- square root of 3x+28)/(x+1)	$lim_{x \to - 1} \frac{5 - \sqrt{3 x + 28}}{x + 1}$
20797	Evaluate the Limit	limit as x approaches 0 of x^3+3x	$lim_{x \to 0} x^{3} + 3 x$
20798	Evaluate the Limit	limit as x approaches 2 of (x^2-x-2)/(x-2)	$lim_{x \to 2} \frac{x^{2} - x - 2}{x - 2}$
20799	Evaluate the Limit	limit as x approaches 0 of x^2sec(x^2)	$lim_{x \to 0} x^{2} \sec (x^{2})$
20800	Evaluate the Limit	limit as x approaches infinity of ( square root of 4x^6-x)/(x^3+2)	$lim_{x \to \infty} \frac{\sqrt{4 x^{6} - x}}{x^{3} + 2}$