Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
65001	Evaluate the Function	f(pi/2)=3sin(3x)	$f (\frac{π}{2}) = 3 \sin (3 x)$
65002	Evaluate the Function	f(pi/2+0.01)=16cos(x)	$f (\frac{π}{2} + 0.01) = 16 \cos (x)$
65003	Find the Derivative Using Product Rule - d/dx	y=(6x-5)^2(3-x^5)^2	$y = {(6 x - 5)}^{2} {(3 - x^{5})}^{2}$
65004	Evaluate the Function	f(7)=(s^3-343)/(s^2-49)	$f (7) = \frac{s^{3} - 343}{s^{2} - 49}$
65005	Evaluate the Function	f(-2)=e^-2	$f (- 2) = e^{- 2}$
65006	Find the Derivative Using Product Rule - d/dx	integral from 0 to 1 of (3x^2-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{2} - x^{2} + 2 x - 4}{\sqrt{x^{2} - 3 x + 2}} d x$
65007	Find the Derivative Using Product Rule - d/dx	integral from 0 to 1 of (3x^3-x^2+2x-4)/( square root of x^2-3x+2) with respect to x	$\int_{0}^{1} \frac{3 x^{3} - x^{2} + 2 x - 4}{\sqrt{x^{2}} - 3 x + 2} d x$
65008	Find the Concavity	y=x^2-2x	$y = x^{2} - 2 x$
65009	Find the Domain and Range	4^(x-3)	$4^{x - 3}$
65010	Find the Inverse	f(x)=x/3	$f (x) = \frac{x}{3}$
65011	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-21x^2	$f (x) = x^{3} - 21 x^{2}$
65012	Find the Inverse	f(x)=1/8x-5	$f (x) = \frac{1}{8} x - 5$
65013	Find Where Increasing/Decreasing Using Derivatives	f(x)=-x^3+6x^2-17	$f (x) = - x^{3} + 6 x^{2} - 17$
65014	Find the Inverse	f(x)=(2x-1)/(x+7)	$f (x) = \frac{2 x - 1}{x + 7}$
65015	Find the Vertex	-3x^2-24x-45	$- 3 x^{2} - 24 x - 45$
65016	Evaluate from the Left	limit as x approaches 1 of ( square root of x-1)/(x-1)	$lim_{x \to 1} \frac{\sqrt{x} - 1}{x - 1}$
65017	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^(2/3)-x	$f (x) = x^{\frac{2}{3}} - x$
65018	Evaluate from the Left	limit as theta approaches -pi of csc(theta)	$lim_{θ \to - π} \csc (θ)$
65019	Evaluate from the Left	limit as x approaches 0 of x^3-1/(x^2)	$lim_{x \to 0} x^{3} - \frac{1}{x^{2}}$
65020	Evaluate from the Left	limit as x approaches -1 of f(x)	$lim_{x \to - 1} f (x)$
65021	Graph the Interval	(-6,6)	$(- 6, 6)$
65022	Find the Second Derivative	(2000x)/(4x+75)	$\frac{2000 x}{4 x + 75}$
65023	Find the Second Derivative	9/x	$\frac{9}{x}$
65024	Find the Second Derivative	(e^x)/(8+e^x)	$\frac{e^{x}}{8 + e^{x}}$
65025	Find the Second Derivative	x^(1/7)	$x^{\frac{1}{7}}$
65026	Find the Second Derivative	x^(1/3)(x+4)	$x^{\frac{1}{3}} (x + 4)$
65027	Find the x and y Intercepts	x^2+x-2	$x^{2} + x - 2$
65028	Find the x and y Intercepts	2x^3-9x^2+12x	$2 x^{3} - 9 x^{2} + 12 x$
65029	Find the Equation of the Circle	r=4sin(theta)	$r = 4 \sin (θ)$
65030	Find the x and y Intercepts	2x^2+9x-5	$2 x^{2} + 9 x - 5$
65031	Evaluate the Derivative at f'(0)	f(x)=x^2+7x-2 ; f'(0)	$f (x) = x^{2} + 7 x - 2$ ; $f' (0)$
65032	Find the Local Maxima and Minima	f(x)=x^4-6x^2-3	$f (x) = x^{4} - 6 x^{2} - 3$
65033	Find the Local Maxima and Minima	g(x)=210+8x^3+x^4	$g (x) = 210 + 8 x^{3} + x^{4}$
65034	Find the Local Maxima and Minima	f(x)=3x^3-3x^2-3x+8	$f (x) = 3 x^{3} - 3 x^{2} - 3 x + 8$
65035	Find the Local Maxima and Minima	f(x)=x^(6/5)-12x^(1/5)	$f (x) = x^{\frac{6}{5}} - 12 x^{\frac{1}{5}}$
65036	Find the Local Maxima and Minima	f(x)=x^3-12x^2+36x+4	$f (x) = x^{3} - 12 x^{2} + 36 x + 4$
65037	Find the Local Maxima and Minima	f(x)=x^3+0.5x^2-2x-4	$f (x) = x^{3} + 0.5 x^{2} - 2 x - 4$
65038	Find the Roots (Zeros)	f(x)=x^2-3x-10	$f (x) = x^{2} - 3 x - 10$
65039	Find the Local Maxima and Minima	f(x)=(x^2+4x+4)(x-1)	$f (x) = (x^{2} + 4 x + 4) (x - 1)$
65040	Find the Local Maxima and Minima	f(x)=(x-7)^3	$f (x) = {(x - 7)}^{3}$
65041	Find the Local Maxima and Minima	f(x)=3x^(2/5)-x^(3/5)	$f (x) = 3 x^{\frac{2}{5}} - x^{\frac{3}{5}}$
65042	Evaluate Using the Given Value	v(13)=25 , 900(0.90)^13	$v (13) = 25$ , $900 {(0.9)}^{13}$
65043	Expand the Logarithmic Expression	log of ( seventh root of r cube root of s)/(u^2)	$\log (\frac{\sqrt[7]{r} \sqrt[3]{s}}{u^{2}})$
65044	Add	-4/(x-1)+(1-3x)/x	$- \frac{4}{x - 1} + \frac{1 - 3 x}{x}$
65045	Find the Inflection Points	5x^3-60x+5	$5 x^{3} - 60 x + 5$
65046	Write in Exponential Form	sum from n=1 to 4 of 3n+1	$\sum_{n = 1}^{4} 3 n + 1$
65047	Find the Second Derivative	y=x^2 natural log of 7x	$y = x^{2} \ln (7 x)$
65048	Find the Second Derivative	y = square root of 7x+3	$y = \sqrt{7 x + 3}$
65049	Find the Second Derivative	x^2+y^2=5	$x^{2} + y^{2} = 5$
65050	Find the Second Derivative	y^5=x^9	$y^{5} = x^{9}$
65051	Find the Second Derivative	s=6t^5-5t^6	$s = 6 t^{5} - 5 t^{6}$
65052	Find dy/dx	y=sin(6x)	$y = \sin (6 x)$
65053	Find dy/dx	y=arcsin(4x^5)	$y = \arcsin (4 x^{5})$
65054	Find dy/dx	y=xcos(x)	$y = x \cos (x)$
65055	Find dy/dx	y=x natural log of x-x	$y = x \ln (x) - x$
65056	Find dy/dx	y=e^(-8x)sin(x)	$y = e^{- 8 x} \sin (x)$
65057	Find dy/dx	y=e^(-7x)sin(x)	$y = e^{- 7 x} \sin (x)$
65058	Find dy/dx	y=x^(- square root of 11)	$y = x^{- \sqrt{11}}$
65059	Find dy/dx	y=x^(sin(x))	$y = x^{\sin (x)}$
65060	Find dy/dx	y=x^0.5	$y = x^{0.5}$
65061	Find dy/dx	y=x^0.6	$y = x^{0.6}$
65062	Find dy/dx	y=x^2sin(2x)	$y = x^{2} \sin (2 x)$
65063	Find dy/dx	y=x^12	$y = x^{12}$
65064	Find dy/dx	y=x^3e^(x^5)	$y = x^{3} e^{x^{5}}$
65065	Find dy/dx	y=x^2-2x-3	$y = x^{2} - 2 x - 3$
65066	Find dy/dx	y=x+1/x	$y = x + \frac{1}{x}$
65067	Evaluate the Summation	sum from 12 to 73 of n	$\sum_{12}^{73} n$
65068	Evaluate the Summation	sum from i=1 to infinity of (4/7)^i	$\sum_{i = 1}^{\infty} {(\frac{4}{7})}^{i}$
65069	Evaluate the Summation	sum from i=1 to infinity of (1/3)^i	$\sum_{i = 1}^{\infty} {(\frac{1}{3})}^{i}$
65070	Evaluate the Summation	sum from i=1 to 1000 of 2i	$\sum_{i = 1}^{1000} 2 i$
65071	Evaluate the Summation	sum from i=1 to 10 of 5i	$\sum_{i = 1}^{10} 5 i$
65072	Evaluate the Summation	sum from i=1 to 21 of (i-8)^2	$\sum_{i = 1}^{21} {(i - 8)}^{2}$
65073	Evaluate the Summation	sum from i=1 to 21 of i(i-1)^2	$\sum_{i = 1}^{21} i {(i - 1)}^{2}$
65074	Evaluate the Summation	sum from i=1 to 14 of i^2	$\sum_{i = 1}^{14} i^{2}$
65075	Evaluate the Summation	sum from i=1 to 15 of 2i	$\sum_{i = 1}^{15} 2 i$
65076	Evaluate the Summation	sum from i=1 to infinity of -4*0.5^(i-1)	$\sum_{i = 1}^{\infty} - 4 {(0.5)}^{i - 1}$
65077	Evaluate the Summation	sum from i=1 to infinity of -7i+22	$\sum_{i = 1}^{\infty} - 7 i + 22$
65078	Evaluate the Summation	sum from i=1 to 10 of 5+1/(2i)	$\sum_{i = 1}^{10} 5 + \frac{1}{2 i}$
65079	Evaluate the Summation	sum from i=1 to 10 of 9i-3	$\sum_{i = 1}^{10} 9 i - 3$
65080	Evaluate the Summation	sum from i=1 to 10 of -3i+7	$\sum_{i = 1}^{10} - 3 i + 7$
65081	Evaluate the Summation	sum from i=1 to infinity of 19*0.03^i	$\sum_{i = 1}^{\infty} 19 {(0.03)}^{i}$
65082	Evaluate the Summation	sum from i=1 to infinity of 1/i	$\sum_{i = 1}^{\infty} \frac{1}{i}$
65083	Evaluate the Summation	sum from i=1 to 8 of 3i-1	$\sum_{i = 1}^{8} 3 i - 1$
65084	Evaluate the Summation	sum from i=1 to 6 of 8i	$\sum_{i = 1}^{6} 8 i$
65085	Evaluate the Summation	sum from j=1 to 5 of (-1)^jj	$\sum_{j = 1}^{5} {(- 1)}^{j} j$
65086	Evaluate the Summation	sum from j=1 to 9 of (-1/4)^j	$\sum_{j = 1}^{9} {(- \frac{1}{4})}^{j}$
65087	Evaluate the Summation	sum from j=1 to infinity of (-3/5)^j	$\sum_{j = 1}^{\infty} {(- \frac{3}{5})}^{j}$
65088	Evaluate the Summation	sum from j=1 to 4 of 54(1/3)^j	$\sum_{j = 1}^{4} 54 {(\frac{1}{3})}^{j}$
65089	Evaluate the Summation	sum from j=1 to 4 of (1/4)^j	$\sum_{j = 1}^{4} {(\frac{1}{4})}^{j}$
65090	Evaluate the Summation	sum from j=1 to 10 of 3j+6	$\sum_{j = 1}^{10} 3 j + 6$
65091	Evaluate the Summation	sum from j=1 to 200 of 2j(j+3)	$\sum_{j = 1}^{200} 2 j (j + 3)$
65092	Evaluate the Summation	sum from j=1 to 38 of j^3-25j	$\sum_{j = 1}^{38} j^{3} - 25 j$
65093	Evaluate the Summation	sum from i=4 to 12 of -8-7i	$\sum_{i = 4}^{12} - 8 - 7 i$
65094	Evaluate the Summation	sum from i=1 to 5 of 2i^2	$\sum_{i = 1}^{5} 2 i^{2}$
65095	Evaluate the Summation	sum from i=1 to 6 of 3i^3	$\sum_{i = 1}^{6} 3 i^{3}$
65096	Evaluate the Summation	sum from i=1 to 5 of 5i-2	$\sum_{i = 1}^{5} 5 i - 2$
65097	Evaluate the Summation	sum from i=1 to 5 of (1/5)^i	$\sum_{i = 1}^{5} {(\frac{1}{5})}^{i}$
65098	Evaluate the Summation	sum from i=1 to 60 of 2i	$\sum_{i = 1}^{60} 2 i$
65099	Evaluate the Summation	sum from i=1 to 54 of 9i+3	$\sum_{i = 1}^{54} 9 i + 3$
65100	Evaluate the Summation	sum from i=1 to 28 of -6i+7	$\sum_{i = 1}^{28} - 6 i + 7$