Calculus questions - page 853

Questions

Rank	Topic	Problem	Formatted Problem
52825	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x+5- square root of x+7)/(x-2)	$lim_{x \to 2} \frac{\sqrt{2 x + 5} - \sqrt{x + 7}}{x - 2}$
52826	Find dy/dx	y=(3x^3+5)/(3+2x)	$y = \frac{3 x^{3} + 5}{3 + 2 x}$
52827	Find Where Increasing/Decreasing	y=7500(1+0.03)^x	$y = 7500 {(1 + 0.03)}^{x}$
52828	Find the Antiderivative	-2/( square root of x)	$- \frac{2}{\sqrt{x}}$
52829	Evaluate the Integral	integral from 0 to natural log of 2 of xe^(-x) with respect to x	$\int_{0}^{\ln (2)} x e^{- x} d x$
52830	Evaluate the Limit	limit as x approaches 0 of (tan(2x)^2)/(xsin(3x))	$lim_{x \to 0} \frac{\tan^{2} (2 x)}{x \sin (3 x)}$
52831	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (e^(-x)-1)/(3tan(2x)-2x^3)	$lim_{x \to 0} \frac{e^{- x} - 1}{3 \tan (2 x) - 2 x^{3}}$
52832	Find Where Increasing/Decreasing	f(x)=-x^4-9x^3-24x^2-16x	$f (x) = - x^{4} - 9 x^{3} - 24 x^{2} - 16 x$
52833	Integrate Using u-Substitution	integral from 0 to 2 of square root of 4-x^2 with respect to x	$\int_{0}^{2} \sqrt{4 - x^{2}} d x$
52834	Evaluate the Integral	integral from 0 to a^(1/2) of x^3 square root of a^2-x^4 with respect to x	$\int_{0}^{a^{\frac{1}{2}}} x^{3} \sqrt{a^{2} - x^{4}} d x$
52835	Find the Derivative - d/dx	-1/(2 square root of x)	$- \frac{1}{2 \sqrt{x}}$
52836	Find dy/dx	y=-5(2x+3)^3	$y = - 5 {(2 x + 3)}^{3}$
52837	Find the Derivative - d/dx	1/((x^2+1)^(3/2))	$\frac{1}{{(x^{2} + 1)}^{\frac{3}{2}}}$
52838	Evaluate the Limit	limit as x approaches -1 of (x^2+yx+z)/(x^2-1)=3	$lim_{x \to - 1} \frac{x^{2} + y x + z}{x^{2} - 1} = 3$
52839	Evaluate the Integral	integral of (-6+x^3) with respect to x	$\int (- 6 + x^{3}) d x$
52840	Evaluate the Integral	integral of xe^x+e^x with respect to x	$\int x e^{x} + e^{x} d x$
52841	Evaluate the Integral	integral from 0 to 1 of (x-1)/(x+1) with respect to x	$\int_{0}^{1} \frac{x - 1}{x + 1} d x$
52842	Find the Derivative - d/dy	1/(x^2+y^2)	$\frac{1}{x^{2} + y^{2}}$
52843	Evaluate the Limit	limit as x approaches 3 of (2x^2-5x-12)/(6-x-x^2)	$lim_{x \to 3} \frac{2 x^{2} - 5 x - 12}{6 - x - x^{2}}$
52844	Find the Derivative - d/dx	y=1/( square root of 1-x^2)	$y = \frac{1}{\sqrt{1 - x^{2}}}$
52845	Find the Derivative - d/dx	-1/( square root of 1-x^2)	$- \frac{1}{\sqrt{1 - x^{2}}}$
52846	Evaluate the Integral	integral from pi/6 to pi/2 of cos(x) with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} \cos (x) d x$
52847	Evaluate the Integral	integral from 1 to 2 of 2x(1+x^2) with respect to x	$\int_{1}^{2} 2 x (1 + x^{2}) d x$
52848	Find the Derivative - d/dx	(x^3-2x^2+x-1)/(x-2)	$\frac{x^{3} - 2 x^{2} + x - 1}{x - 2}$
52849	Find the Derivative - d/dy	x*y	$x \cdot y$
52850	Evaluate the Integral	integral from pi/2 to (3pi)/2 of xsin(x) with respect to x	$\int_{\frac{π}{2}}^{\frac{3 π}{2}} x \sin (x) d x$
52851	Find the Percentage Rate of Change	w(t)=700(0.995)^t	$w (t) = 700 {(0.995)}^{t}$
52852	Find the Antiderivative	square root of 5-x	$\sqrt{5 - x}$
52853	Evaluate the Integral	integral from -3 to 4 of (2e^(-3x)-3e^x) with respect to x	$\int_{- 3}^{4} (2 e^{- 3 x} - 3 e^{x}) d x$
52854	Find the Critical Points	Let h(x)=e^(2x-6)-e	Let $h (x) = e^{2 x - 6} - e$
52855	Find the Absolute Max and Min over the Interval	f(x)=\|x\|-3\|x+1\| , [-2,2]	$f (x) = \| x \| - 3 \| x + 1 \|$ , $[- 2, 2]$
52856	Find dx/dy	tan(xy)=x	$\tan (x y) = x$
52857	Find the Derivative of the Integral	integral from -19 to x^2 of (t-169)^92(5t-245)^37 with respect to t	$\int_{- 19}^{x^{2}} {(t - 169)}^{92} {(5 t - 245)}^{37} d t$
52858	Find dy/dx	y = square root of x^2+2x-1	$y = \sqrt{x^{2} + 2 x - 1}$
52859	Integrate Using u-Substitution	integral of square root of 1+x^2 with respect to x	$\int \sqrt{1 + x^{2}} d x$
52860	Evaluate the Integral	integral of -1/(x^2) with respect to x	$\int \frac{- 1}{x^{2}} d x$
52861	Find the Derivative - d/dx	y=((x^2+1)^2)/(2x^2)	$y = \frac{{(x^{2} + 1)}^{2}}{2 x^{2}}$
52862	Find the Second Derivative	y=-1/5x^-4+1/2x^3-3x^-1	$y = - \frac{1}{5} x^{- 4} + \frac{1}{2} x^{3} - 3 x^{- 1}$
52863	Find Where Increasing/Decreasing	f(x)=-((x-2)^2)/((x-1)^2)	$f (x) = - \frac{{(x - 2)}^{2}}{{(x - 1)}^{2}}$
52864	Find the Derivative - d/dx	2e^(2x)-e^(-x)	$2 e^{2 x} - e^{- x}$
52865	Evaluate the Integral	integral of (3(1-tan(x)^2))/(sec(x)^2) with respect to x	$\int \frac{3 (1 - \tan^{2} (x))}{\sec^{2} (x)} d x$
52866	Find dy/dx	x^2=4y^3+5y^2	$x^{2} = 4 y^{3} + 5 y^{2}$
52867	Find the Antiderivative	fifth root of x-2e^x	$\sqrt[5]{x} - 2 e^{x}$
52868	Evaluate the Integral	integral of (2 square root of x^3+7 cube root of x^2) with respect to x	$\int (2 \sqrt{x^{3}} + 7 \sqrt[3]{x^{2}}) d x$
52869	Find the Derivative - d/dt	17/2-3/2cos((pit)/6)	$\frac{17}{2} - \frac{3}{2} \cos (\frac{π t}{6})$
52870	Find the Center and Radius	x^2-10x=-y^2+16y-40	$x^{2} - 10 x = - y^{2} + 16 y - 40$
52871	Find dx/dy	(x+y)^2(x-y)^2=x^4+y^4	${(x + y)}^{2} {(x - y)}^{2} = x^{4} + y^{4}$
52872	Evaluate the Integral	integral of (-3x^-2+4+6x^3) with respect to x	$\int (- 3 x^{- 2} + 4 + 6 x^{3}) d x$
52873	Find the Antiderivative	f(x)=7-6x^2+12x^3	$f (x) = 7 - 6 x^{2} + 12 x^{3}$
52874	Evaluate the Integral	e^( integral of -1 with respect to x)	$e^{\int - 1 d x}$
52875	Evaluate the Summation	4 sum from k=3 to 6 of -k^2+2k	$4 \sum_{k = 3}^{6} - k^{2} + 2 k$
52876	Find dy/dx	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
52877	Evaluate the Limit	limit as x approaches 3 of (x+9)/(5-x)	$lim_{x \to 3} \frac{x + 9}{5 - x}$
52878	Find dx/dy	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
52879	Evaluate the Integral	4 integral of 1/(1-x^2) with respect to x	$4 \int \frac{1}{1 - x^{2}} d x$
52880	Find the Derivative - d/dx	3e^x-e^(2x)	$3 e^{x} - e^{2 x}$
52881	Find the Derivative - d/dx	(cos(x)^2)	$(\cos^{2} (x))$
52882	Find the Derivative - d/dx	10-1/5(x-6)^2	$10 - \frac{1}{5} {(x - 6)}^{2}$
52883	Evaluate the Limit	limit as x approaches 1/2 of (2x-5)/7	$lim_{x \to \frac{1}{2}} \frac{2 x - 5}{7}$
52884	Find the Derivative - d/df	f(x)^2	$f {(x)}^{2}$
52885	Find the Antiderivative	e^(2x-1)*y^-2	$e^{2 x - 1} \cdot y^{- 2}$
52886	Find the Derivative - d/dx	y=( square root of x^3+ square root of x^5)^n	$y = {(\sqrt{x^{3}} + \sqrt{x^{5}})}^{n}$