Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68601	Evaluate the Limit	limit as x approaches -1 of (x^2-1)/(-2x-2)	$lim_{x \to - 1} \frac{x^{2} - 1}{- 2 x - 2}$
68602	Find the Derivative - d/dx	arcsin(x/3)	$\arcsin (\frac{x}{3})$
68603	Integrate Using u-Substitution	integral of square root of 2x+1 with respect to x	$\int \sqrt{2 x + 1} d x$
68604	Find the Second Derivative	x/y	$\frac{x}{y}$
68605	Find the Derivative - d/dX	(X-2)^4	${(X - 2)}^{4}$
68606	Evaluate the Integral	integral of (2+3x^2-8x^3) with respect to x	$\int (2 + 3 x^{2} - 8 x^{3}) d x$
68607	Find the Slope	f(x)=5x-2	$f (x) = 5 x - 2$
68608	Find the Derivative - d/dx	y=2/(e^x)	$y = \frac{2}{e^{x}}$
68609	Find the Derivative - d/dx	(x^2)/(1+x^2)	$\frac{x^{2}}{1 + x^{2}}$
68610	Evaluate the Limit	limit as t approaches -3 of (6+4t)/(t^2+1)	$lim_{t \to - 3} \frac{6 + 4 t}{t^{2} + 1}$
68611	Find the Tangent Line at (3,0)	y = natural log of x^2-3x+1 , (3,0)	$y = \ln (x^{2} - 3 x + 1)$ , $(3, 0)$
68612	Evaluate the Limit	limit as x approaches negative infinity of x/( square root of x^2+4)	$lim_{x \to - \infty} \frac{x}{\sqrt{x^{2} + 4}}$
68613	Find the Derivative - d/dx	y=2a-bx	$y = 2 a - b x$
68614	Find the Slope	f(x)=2x+3	$f (x) = 2 x + 3$
68615	Evaluate the Integral	integral from 0 to 2 of (2x+1)^3*2 with respect to x	$\int_{0}^{2} {(2 x + 1)}^{3} \cdot 2 d x$
68616	Evaluate the Integral	integral of x/( square root of 1-x^4) with respect to x	$\int \frac{x}{\sqrt{1 - x^{4}}} d x$
68617	Find dy/dx	y=x/(x+1)	$y = \frac{x}{x + 1}$
68618	Find the Integral	f(x)=6-3x	$f (x) = 6 - 3 x$
68619	Find dy/du	y = square root of u	$y = \sqrt{u}$
68620	Find dy/dx	x^3+y^3=12xy-8	$x^{3} + y^{3} = 12 x y - 8$
68621	Evaluate the Limit	limit as x approaches 0 of (cos(4x)sin(3x))/(5x)	$lim_{x \to 0} \frac{\cos (4 x) \sin (3 x)}{5 x}$
68622	Find dy/dx	y=(x^2-3x+2)/(x^7-2)	$y = \frac{x^{2} - 3 x + 2}{x^{7} - 2}$
68623	Find the Maximum/Minimum Value	h(x)=(x-1) square root of x	$h (x) = (x - 1) \sqrt{x}$
68624	Evaluate the Integral	integral of ( square root of x+ cube root of x) with respect to x	$\int (\sqrt{x} + \sqrt[3]{x}) d x$
68625	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (x^2+3x+12)/(-6 natural log of x^3)	$lim_{x \to \infty} \frac{x^{2} + 3 x + 12}{- 6 \ln (x^{3})}$
68626	Find the Derivative - d/dx	xe^(y/z)	$x e^{\frac{y}{z}}$
68627	Find the Domain and Range	f(x)=x+3 if -2<=x<1; 7 if x=1; -x+2 if x>1	$f (x) = {\begin{cases} x + 3 & - 2 \leq x < 1 \\ 7 & x = 1 \\ - x + 2 & x > 1 \end{cases}$
68628	Solve the Differential Equation	(y^2+xy^2)(dy)/(dx)=1	$(y^{2} + x y^{2}) \frac{d y}{d x} = 1$
68629	Find the Derivative - d/dx	y = square root of x^2	$y = \sqrt{x^{2}}$
68630	Evaluate the Limit	limit as x approaches a of (x^2-(a+1)x+a)/(x^3-a^3)	$lim_{x \to a} \frac{x^{2} - (a + 1) x + a}{x^{3} - a^{3}}$
68631	Find the Derivative - d/dx	d/(dx)(x/(cos(x)))	$\frac{d}{d x} (\frac{x}{\cos (x)})$
68632	Check if Differentiable Over an Interval	f(x)=1/x , [2,6]	$f (x) = \frac{1}{x}$ , $[2, 6]$
68633	Find dy/dx	3x^3+9xy^2=5x^3	$3 x^{3} + 9 x y^{2} = 5 x^{3}$
68634	Find dy/dx	y=(4x+3)^5	$y = {(4 x + 3)}^{5}$
68635	Find the Second Derivative	y=6x^4-3x^3+x^2-5	$y = 6 x^{4} - 3 x^{3} + x^{2} - 5$
68636	Find dy/dx	y^2-x^3=41	$y^{2} - x^{3} = 41$
68637	Find dy/dx	y=tan(x)-cot(x)	$y = \tan (x) - \cot (x)$
68638	Find the Domain and Range	f(x)=3+3x if x<0; x^2 if x>=0	$f (x) = {\begin{cases} 3 + 3 x & x < 0 \\ x^{2} & x \geq 0 \end{cases}$
68639	Evaluate the Limit	limit as x approaches negative infinity of ( square root of x^2-9)/(2x-6)	$lim_{x \to - \infty} \frac{\sqrt{x^{2} - 9}}{2 x - 6}$
68640	Find the Derivative - d/dx	d/(dx)xy	$\frac{d}{d x} x y$
68641	Evaluate the Limit	limit as x approaches 0 of ( square root of 4^2+x-4)/x	$lim_{x \to 0} \frac{\sqrt{4^{2} + x} - 4}{x}$
68642	Find the Derivative - d/dx	y=(4-x)(3+x)	$y = (4 - x) (3 + x)$
68643	Find the Domain and Range	f(x)=x^2+4x if x<-3; 2 if x>=-3	$f (x) = {\begin{cases} x^{2} + 4 x & x < - 3 \\ 2 & x \geq - 3 \end{cases}$
68644	Find the Maximum/Minimum Value	y=(x-2)^2	$y = {(x - 2)}^{2}$
68645	Evaluate the Limit	limit as x approaches 0 of ( square root of 3^2+x-3)/x	$lim_{x \to 0} \frac{\sqrt{3^{2} + x} - 3}{x}$
68646	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of tan(4x)^x	$lim_{x \to 0^{+}} {\tan (4 x)}^{x}$
68647	Evaluate the Integral	integral of (x^4-x^3+x^2) with respect to x	$\int (x^{4} - x^{3} + x^{2}) d x$
68648	Find dy/dx	y=6x	$y = 6 x$
68649	Find the Derivative - d/dx	(dx)/x	$\frac{d x}{x}$
68650	Evaluate the Integral	integral of (tan(x)^2+cot(x)^2+4) with respect to x	$\int (\tan^{2} (x) + \cot^{2} (x) + 4) d x$
68651	Find the Derivative - d/dt	t^-2	$t^{- 2}$
68652	Find dy/dx	y=a^x	$y = a^{x}$
68653	Evaluate the Limit	limit as x approaches -2 of (x^2-4)/(-3x-6)	$lim_{x \to - 2} \frac{x^{2} - 4}{- 3 x - 6}$
68654	Find dy/dx	y = square root of 3+x^2	$y = \sqrt{3 + x^{2}}$
68655	Evaluate the Limit	limit as t approaches 0 of ( square root of t^2+4^2-4)/(t^2)	$lim_{t \to 0} \frac{\sqrt{t^{2} + 4^{2}} - 4}{t^{2}}$
68656	Find the Antiderivative	u	$u$
68657	Integrate Using u-Substitution	integral of ( natural log of x)/x with respect to x	$\int \frac{\ln (x)}{x} d x$
68658	Evaluate the Integral	integral from -1 to 1 of (3x^3-x^2+x-1) with respect to x	$\int_{- 1}^{1} (3 x^{3} - x^{2} + x - 1) d x$
68659	Find the Derivative - d/dx	(x^2+y^2)	$(x^{2} + y^{2})$
68660	Evaluate the Limit	limit as x approaches 0 from the right of 1/x-1/(x^2)	$lim_{x \to 0^{+}} \frac{1}{x} - \frac{1}{x^{2}}$
68661	Find dy/dx	e^(2y)+x^3=y	$e^{2 y} + x^{3} = y$
68662	Evaluate the Integral	integral from pi/4 to pi/2 of (2-csc(x)^2) with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{2}} (2 - \csc^{2} (x)) d x$
68663	Find the Derivative - d/dx	e^x-cos(x)	$e^{x} - \cos (x)$
68664	Evaluate the Limit	limit as x approaches 1 of (2x-2)/(x^2-1)	$lim_{x \to 1} \frac{2 x - 2}{x^{2} - 1}$
68665	Find dy/dx	y=2e^x	$y = 2 e^{x}$
68666	Evaluate the Integral	integral of (2x^6-5x^4+4x^2-6) with respect to x	$\int (2 x^{6} - 5 x^{4} + 4 x^{2} - 6) d x$
68667	Find the Area Under the Curve	f(x)=x^2	$f (x) = x^{2}$
68668	Find the Antiderivative	square root of 5	$\sqrt{5}$
68669	Find dy/dx	y = fourth root of x	$y = \sqrt[4]{x}$
68670	Find the Derivative - d/dt	ty	$t y$
68671	Find the Center and Radius	(x^2)/144+(y^2)/169=1	$\frac{x^{2}}{144} + \frac{y^{2}}{169} = 1$
68672	Evaluate the Limit	limit as x approaches 0 from the left of x/(\|x\|)=-1	$lim_{x \to 0^{-}} \frac{x}{\| x \|} = - 1$
68673	Find the Derivative - d/dx	1/(x^2)+1/x+x	$\frac{1}{x^{2}} + \frac{1}{x} + x$
68674	Find the Derivative - d/dx	y=x^5f(x)	$y = x^{5} f (x)$
68675	Evaluate the Limit	limit as x approaches -4 of (5x+25)/(x^2-2x)	$lim_{x \to - 4} \frac{5 x + 25}{x^{2} - 2 x}$
68676	Find Where Increasing/Decreasing	F(x)=x square root of 6-x	$F (x) = x \sqrt{6 - x}$
68677	Find the Derivative - d/dx	y=4/(x^-3)	$y = \frac{4}{x^{- 3}}$
68678	Find the Derivative - d/dz	xyz	$x y z$
68679	Find the Derivative - d/dx	d/(dx)((e^x)/(cos(x)))	$\frac{d}{d x} (\frac{e^{x}}{\cos (x)})$
68680	Find dy/dx	xy^2+2xy=8	$x y^{2} + 2 x y = 8$
68681	Evaluate the Limit	limit as x approaches 0 of (-10x+cos(-2x)-1)/(-10x)	$lim_{x \to 0} \frac{- 10 x + \cos (- 2 x) - 1}{- 10 x}$
68682	Find dy/dx	y=( natural log of x)/(x^4)	$y = \frac{\ln (x)}{x^{4}}$
68683	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of tan(3x)^x	$lim_{x \to 0^{+}} {\tan (3 x)}^{x}$
68684	Integrate Using u-Substitution	integral of x square root of 1-x^2 with respect to x	$\int x \sqrt{1 - x^{2}} d x$
68685	Evaluate the Limit	limit as x approaches infinity of (5x^3+2x^2-1)/(2x+3)	$lim_{x \to \infty} \frac{5 x^{3} + 2 x^{2} - 1}{2 x + 3}$
68686	Evaluate the Integral	integral of (1-x^4) with respect to x	$\int (1 - x^{4}) d x$
68687	Find dy/dx	y=x/(1-x^3)	$y = \frac{x}{1 - x^{3}}$
68688	Find the Third Derivative	f(x)=2x^2-3x^2+6x-1	$f (x) = 2 x^{2} - 3 x^{2} + 6 x - 1$
68689	Evaluate the Integral	integral of 5tan(x)^3sec(x) with respect to x	$\int 5 \tan^{3} (x) \sec (x) d x$
68690	Evaluate the Limit	limit as x approaches 0 of (2(x+h)^3-2x^3)/h	$lim_{x \to 0} \frac{2 {(x + h)}^{3} - 2 x^{3}}{h}$
68691	Find dy/dx	3x^2y^2=4x^2-4xy	$3 x^{2} y^{2} = 4 x^{2} - 4 x y$
68692	Find the Antiderivative	h(x)=sin(x)+cos(x)-sec(x)^2	$h (x) = \sin (x) + \cos (x) - \sec^{2} (x)$
68693	Find the Derivative - d/dx	(xy)	$(x y)$
68694	Find dy/dx	y=6^x	$y = 6^{x}$
68695	Find the Derivative - d/dx	(3-2x^2)^2 square root of 2x^2+1	${(3 - 2 x^{2})}^{2} \sqrt{2 x^{2} + 1}$
68696	Evaluate the Limit	limit as h approaches -2 of (h^2-2^2)/(2h^2+5h+2)	$lim_{h \to - 2} \frac{h^{2} - 2^{2}}{2 h^{2} + 5 h + 2}$
68697	Find the Derivative - d/dx	d/(dx)(cos(x)x^2)	$\frac{d}{d x} (\cos (x) x^{2})$
68698	Find dy/dx	e^(xy)=3y	$e^{x y} = 3 y$
68699	Evaluate the Integral	integral of (4-x) with respect to x	$\int (4 - x) d x$
68700	Evaluate the Integral	integral of ( square root of x+1/(5 square root of x)) with respect to x	$\int (\sqrt{x} + \frac{1}{5 \sqrt{x}}) d x$