Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
68801	Find the Maximum/Minimum Value	f(x)=(x^2)/(x-4)	$f (x) = \frac{x^{2}}{x - 4}$
68802	Find the Domain and Range	f(x)=-3x+5 if x<1; 4x-2 if x>=1	$f (x) = {\begin{cases} - 3 x + 5 & x < 1 \\ 4 x - 2 & x \geq 1 \end{cases}$
68803	Find dy/dx	y=( natural log of x)/(x^13)	$y = \frac{\ln (x)}{x^{13}}$
68804	Solve the Differential Equation	(dy)/(dx)=x square root of y	$\frac{d y}{d x} = x \sqrt{y}$
68805	Evaluate the Integral	integral of (3x^3-5x^2+3x+4) with respect to x	$\int (3 x^{3} - 5 x^{2} + 3 x + 4) d x$
68806	Find the Derivative - d/dx	e^(-x)cos(x^2)	$e^{- x} \cos (x^{2})$
68807	Evaluate the Limit	limit as x approaches 2 of (sin(x-2))/(x^2-3x+2)	$lim_{x \to 2} \frac{\sin (x - 2)}{x^{2} - 3 x + 2}$
68808	Find the Derivative - d/dx	y=1/( square root of x)+ square root of x	$y = \frac{1}{\sqrt{x}} + \sqrt{x}$
68809	Find the Area Under the Curve	y=4-x^2	$y = 4 - x^{2}$
68810	Evaluate the Integral	integral of 2tan(x)^3sec(x) with respect to x	$\int 2 \tan^{3} (x) \sec (x) d x$
68811	Find dx/dy	square root of x+ square root of y=1	$\sqrt{x} + \sqrt{y} = 1$
68812	Find the Derivative - d/dx	e^xdx	$e^{x} d x$
68813	Find dy/dx	y=x^(5x)	$y = x^{5 x}$
68814	Solve the Differential Equation	(dy)/(dx)=xy^2	$\frac{d y}{d x} = x y^{2}$
68815	Find the Maximum/Minimum Value	y=x^4+4x^3	$y = x^{4} + 4 x^{3}$
68816	Find the Derivative - d/dx	e^(-1/(x^2))	$e^{- \frac{1}{x^{2}}}$
68817	Find dy/dx	y=cos(x^2)	$y = \cos (x^{2})$
68818	Find the Domain and Range	f(x)=-x^2+4 if -3<=x<0; 4 if 0<=x<3; -x+5 if x>=3	$f (x) = {\begin{cases} - x^{2} + 4 & - 3 \leq x < 0 \\ 4 & 0 \leq x < 3 \\ - x + 5 & x \geq 3 \end{cases}$
68819	Evaluate the Integral	integral of 3^(x+2) with respect to x	$\int 3^{x + 2} d x$
68820	Evaluate the Integral	integral of (x^3+x)/(x-1) with respect to x	$\int \frac{x^{3} + x}{x - 1} d x$
68821	Find dy/dx	y = square root of sin(x)	$y = \sqrt{\sin (x)}$
68822	Evaluate the Summation	sum from j=1 to 15 of (j-1)^3	$\sum_{j = 1}^{15} {(j - 1)}^{3}$
68823	Find dy/dx	2y^3+4x^2-y=x^6	$2 y^{3} + 4 x^{2} - y = x^{6}$
68824	Evaluate the Limit	limit as x approaches infinity of (2x^-1+3x^-2)/(x^-2+4)	$lim_{x \to \infty} \frac{2 x^{- 1} + 3 x^{- 2}}{x^{- 2} + 4}$
68825	Find the Derivative - d/dx	square root of x+ square root of y	$\sqrt{x} + \sqrt{y}$
68826	Find the Linearization at a=0	f(x) = square root of 4-x at a=0	$f (x) = \sqrt{4 - x}$ at $a = 0$
68827	Evaluate the Integral	integral from 0 to 2 of (2+x) with respect to x	$\int_{0}^{2} (2 + x) d x$
68828	Find dy/dx	y=1/(x^7)	$y = \frac{1}{x^{7}}$
68829	Find dy/dx	y=e^(-x^2)	$y = e^{- x^{2}}$
68830	Find the Derivative - d/dx	d/(dx)(-2x^5-3x^3+1)	$\frac{d}{d x} (- 2 x^{5} - 3 x^{3} + 1)$
68831	Find the Maximum/Minimum Value	f(x)=e^(2x)+e^(-x)	$f (x) = e^{2 x} + e^{- x}$
68832	Find dx/dy	y=2x^2	$y = 2 x^{2}$
68833	Find dy/dx	x-2x^5y^4=1	$x - 2 x^{5} y^{4} = 1$
68834	Integrate Using Trig Substitution	integral of 1/( square root of 5-7x^2) with respect to x	$\int \frac{1}{\sqrt{5 - 7 x^{2}}} d x$
68835	Evaluate the Integral	integral of ( square root of x+1/(6 square root of x)) with respect to x	$\int (\sqrt{x} + \frac{1}{6 \sqrt{x}}) d x$
68836	Evaluate the Limit	limit as x approaches 2 from the left of (x^2-4)/(x-2)	$lim_{x \to 2^{-}} \frac{x^{2} - 4}{x - 2}$
68837	Evaluate the Limit	limit as x approaches -1 of (x^4+3x^3-x^2+x+4)/(x+1)	$lim_{x \to - 1} \frac{x^{4} + 3 x^{3} - x^{2} + x + 4}{x + 1}$
68838	Evaluate the Integral	integral of (3u^5-2u^3) with respect to u	$\int (3 u^{5} - 2 u^{3}) d u$
68839	Find the Derivative - d/dx	(e^x)/(x^2+1)	$\frac{e^{x}}{x^{2} + 1}$
68840	Find dy/dx	y=x/(e^x)	$y = \frac{x}{e^{x}}$
68841	Find the Derivative - d/dx	d/(dx)(1/(x^9))	$\frac{d}{d x} (\frac{1}{x^{9}})$
68842	Evaluate the Limit	limit as x approaches 1/2 of (x^-1-2)/(x-1/2)	$lim_{x \to \frac{1}{2}} \frac{x^{- 1} - 2}{x - \frac{1}{2}}$
68843	Evaluate the Integral	integral from 0 to infinity of 8e^(-8x) with respect to x	$\int_{0}^{\infty} 8 e^{- 8 x} d x$
68844	Find the Derivative - d/dx	1/(x^3)-2/(x^2)	$\frac{1}{x^{3}} - \frac{2}{x^{2}}$
68845	Find the Derivative - d/dy	(y^2)/x	$\frac{y^{2}}{x}$
68846	Find dy/dx	x^(1/2)+y^(1/2)=9	$x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9$
68847	Find dy/dx	6 square root of y=x-5y	$6 \sqrt{y} = x - 5 y$
68848	Evaluate the Integral	integral of (3x^5-2x^3+5x^2-2)/(x^3+1) with respect to x	$\int \frac{3 x^{5} - 2 x^{3} + 5 x^{2} - 2}{x^{3} + 1} d x$
68849	Evaluate the Limit	limit as x approaches -1/3 of (9x^2-1)/(6x^2+5x+1)	$lim_{x \to - \frac{1}{3}} \frac{9 x^{2} - 1}{6 x^{2} + 5 x + 1}$
68850	Evaluate the Integral	integral from 0 to 5 of 1/( cube root of 5-x) with respect to x	$\int_{0}^{5} \frac{1}{\sqrt[3]{5 - x}} d x$
68851	Find dx/dt	x=e^t	$x = e^{t}$
68852	Find dy/dx	y=x square root of x^2+1	$y = x \sqrt{x^{2} + 1}$
68853	Evaluate the Limit	limit as x approaches 1 of (5x^4+3^x)/( square root of x)	$lim_{x \to 1} \frac{5 x^{4} + 3^{x}}{\sqrt{x}}$
68854	Find the Relative Extrema	f(x)=x^4-12x^3	$f (x) = x^{4} - 12 x^{3}$
68855	Find the Derivative - d/dθ	sec(theta)-cos(theta)	$\sec (θ) - \cos (θ)$
68856	Find the Percentage Rate of Change	y=26(0.989)^x	$y = 26 {(0.989)}^{x}$
68857	Evaluate the Limit	limit as x approaches 4 of (3( natural log of 9x+10+1))/(4((2x+2)^(1/3)+1))	$lim_{x \to 4} \frac{3 (\ln (9 x + 10) + 1)}{4 ({(2 x + 2)}^{\frac{1}{3}} + 1)}$
68858	Find the Derivative - d/dx	y = square root of a^2+x^2	$y = \sqrt{a^{2} + x^{2}}$
68859	Evaluate the Limit	limit as x approaches 1 of ( square root of x-1)/( cube root of x-1)	$lim_{x \to 1} \frac{\sqrt{x} - 1}{\sqrt[3]{x} - 1}$
68860	Find the Derivative - d/dx	y=( square root of x)/(e^x)	$y = \frac{\sqrt{x}}{e^{x}}$
68861	Evaluate the Integral	integral of (4x^2-5)^2*8x with respect to x	$\int {(4 x^{2} - 5)}^{2} \cdot 8 x d x$
68862	Find the Derivative - d/dx	y=csc(x)(x+cot(x))	$y = \csc (x) (x + \cot (x))$
68863	Find the Derivative - d/dx	ex^2	$e x^{2}$
68864	Find dy/dx	x^2+3xy+y^3=10	$x^{2} + 3 x y + y^{3} = 10$
68865	Find the Percentage Rate of Change	y=3100(0.365)^x	$y = 3100 {(0.365)}^{x}$
68866	Evaluate the Limit	limit as x approaches 3 of (4x^2+x-39)/(x^2-9)	$lim_{x \to 3} \frac{4 x^{2} + x - 39}{x^{2} - 9}$
68867	Find Where Increasing/Decreasing	C(x)=x^(1/3)(x+4)	$C (x) = x^{\frac{1}{3}} (x + 4)$
68868	Find dy/dx	1=3x+2x^2y^2	$1 = 3 x + 2 x^{2} y^{2}$
68869	Evaluate the Integral	integral of ( square root of natural log of x)/x with respect to x	$\int \frac{\sqrt{\ln (x)}}{x} d x$
68870	Find the Absolute Max and Min over the Interval	f(x)=9sin(x)+9cos(x) , 0<=x<=2pi	$f (x) = 9 \sin (x) + 9 \cos (x)$ , $0 \leq x \leq 2 π$
68871	Find the Derivative - d/dx	x^3+y^3=6xy	$x^{3} + y^{3} = 6 x y$
68872	Find dy/dx	x^3+x^2y+4y^2=6	$x^{3} + x^{2} y + 4 y^{2} = 6$
68873	Find dy/dx	x^2y+xy^2=3x	$x^{2} y + x y^{2} = 3 x$
68874	Find the Derivative - d/dx	d/(dx)(8sin(x)-x)	$\frac{d}{d x} (8 \sin (x) - x)$
68875	Find the Slope	-2/5	$- \frac{2}{5}$
68876	Find dy/dx	y=3x^3	$y = 3 x^{3}$
68877	Find the Derivative - d/dx	1+cot(x)	$1 + \cot (x)$
68878	Find the Derivative - d/dx	d/(dx)(5/x natural log of x)	$\frac{d}{d x} (\frac{5}{x} \ln (x))$
68879	Find dy/dx	y=x^9	$y = x^{9}$
68880	Find the Maximum/Minimum Value	y=x^3-6x^2	$y = x^{3} - 6 x^{2}$
68881	Integrate Using Trig Substitution	integral of ( square root of 1+x^2)/x with respect to x	$\int \frac{\sqrt{1 + x^{2}}}{x} d x$
68882	Find the Derivative - d/dx	d/(dx)(1/(x^4)-3/(x^2))	$\frac{d}{d x} (\frac{1}{x^{4}} - \frac{3}{x^{2}})$
68883	Find dy/dx	x^2+y^2=81	$x^{2} + y^{2} = 81$
68884	Find dz/dy	z=e^(xy)	$z = e^{x y}$
68885	Find Where Increasing/Decreasing	f(x)=1/3x^3-3/2x^2	$f (x) = \frac{1}{3} x^{3} - \frac{3}{2} x^{2}$
68886	Evaluate the Integral	integral of (x^1.3+7x^2.5) with respect to x	$\int (x^{1.3} + 7 x^{2.5}) d x$
68887	Evaluate the Integral	integral of (3x^2-2x+1)/( square root of x) with respect to x	$\int \frac{3 x^{2} - 2 x + 1}{\sqrt{x}} d x$
68888	Find the Derivative - d/dx	(4x^2+3x)/(2x-7)	$\frac{4 x^{2} + 3 x}{2 x - 7}$
68889	Find the Tangent Line at (0,3)	y=x^4+3e^x , (0,3)	$y = x^{4} + 3 e^{x}$ , $(0, 3)$
68890	Find dy/dx	y=sin(cos(x))	$y = \sin (\cos (x))$
68891	Evaluate the Integral	integral from -2 to -1 of (u-1/(u^2)) with respect to u	$\int_{- 2}^{- 1} (u - \frac{1}{u^{2}}) d u$
68892	Evaluate the Integral	integral of (( square root of a- square root of x)^2)/( square root of x) with respect to x	$\int \frac{{(\sqrt{a} - \sqrt{x})}^{2}}{\sqrt{x}} d x$
68893	Find the Derivative - d/dθ	1-sin(theta)	$1 - \sin (θ)$
68894	Evaluate the Limit	limit as x approaches infinity of square root of xe^(-x/2)	$lim_{x \to \infty} \sqrt{x} e^{- \frac{x}{2}}$
68895	Find the Maximum/Minimum Value	y=(x^3)/3-3x^2-7x	$y = \frac{x^{3}}{3} - 3 x^{2} - 7 x$
68896	Evaluate the Integral	integral from negative infinity to infinity of f(x) with respect to x	$\int_{- \infty}^{\infty} f (x) d x$
68897	Find dy/dx	3x+xy=y	$3 x + x y = y$
68898	Evaluate the Limit	limit as x approaches -4 of ( square root of 5- square root of x+9)/(x+4)	$lim_{x \to - 4} \frac{\sqrt{5} - \sqrt{x + 9}}{x + 4}$
68899	Evaluate the Integral	integral of (x^2-6) with respect to x	$\int (x^{2} - 6) d x$
68900	Integrate Using u-Substitution	integral of x/(x^2+1) with respect to x , u=x^2+1	$\int \frac{x}{x^{2} + 1} d x$ , $u = x^{2} + 1$