Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
1901	Evaluate the Integral	integral from 1 to 7 of ( natural log of (x)^2)/(x^3) with respect to x	$\int_{1}^{7} \frac{\ln ({(x)}^{2})}{x^{3}} d x$
1902	Evaluate the Integral	integral from 0 to 4pi of t^2sin(2t) with respect to t	$\int_{0}^{4 π} t^{2} \sin (2 t) d t$
1903	Evaluate the Integral	integral of (x^2-5x)e^x with respect to x	$\int (x^{2} - 5 x) e^{x} d x$
1904	Evaluate the Integral	integral of x^2-9x+2 with respect to x	$\int x^{2} - 9 x + 2 d x$
1905	Evaluate the Integral	integral from 0 to 1 of (x^2+8)e^(-x) with respect to x	$\int_{0}^{1} (x^{2} + 8) e^{- x} d x$
1906	Evaluate the Integral	integral of (e^t+1)^2 with respect to t	$\int {(e^{t} + 1)}^{2} d t$
1907	Evaluate the Integral	integral of sec(x)tan(x) with respect to x	$\int \sec (x) \tan (x) d x$
1908	Evaluate the Integral	integral of x^(-1/2) with respect to x	$\int x^{- \frac{1}{2}} d x$
1909	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (1-2x)^(1/x)	$lim_{x \to 0} {(1 - 2 x)}^{\frac{1}{x}}$
1910	Evaluate the Summation	sum from i=1 to 20 of (i-1)^2	$\sum_{i = 1}^{20} {(i - 1)}^{2}$
1911	Evaluate the Limit	limit as x approaches 81 of ( square root of x-9)/(x-81)	$lim_{x \to 81} \frac{\sqrt{x} - 9}{x - 81}$
1912	Find the 2nd Derivative	e^(2x)	$e^{2 x}$
1913	Find the Derivative - d/dx	x(7+2x)	$x (7 + 2 x)$
1914	Find the Derivative - d/dx	y=1/(x^8)	$y = \frac{1}{x^{8}}$
1915	Find the Derivative - d/dx	fifth root of x^2	$\sqrt[5]{x^{2}}$
1916	Find the Derivative - d/dx	y=8x-x^2	$y = 8 x - x^{2}$
1917	Find the Derivative - d/dx	cos(a^7+x^7)	$\cos (a^{7} + x^{7})$
1918	Evaluate the Limit	limit as a approaches -2 of F(a)	$lim_{a \to - 2} F (a)$
1919	Find the Derivative - d/dx	fourth root of x^5	$\sqrt[4]{x^{5}}$
1920	Find dy/dx	(2x+2y)^3=8x^3+8y^3	${(2 x + 2 y)}^{3} = 8 x^{3} + 8 y^{3}$
1921	Find dy/dx	xy+x+y=x^2y^2	$x y + x + y = x^{2} y^{2}$
1922	Evaluate the Limit	limit as x approaches 8 of xsin(2/x)	$lim_{x \to 8} x \sin (\frac{2}{x})$
1923	Evaluate the Limit	limit as x approaches -6 of (x^2-36)/(x+6)	$lim_{x \to - 6} \frac{x^{2} - 36}{x + 6}$
1924	Evaluate the Limit	limit as x approaches -3 of (x^3+27)/(x+3)	$lim_{x \to - 3} \frac{x^{3} + 27}{x + 3}$
1925	Evaluate the Limit	limit as x approaches 3 of (x-3)/(x^2-9)	$lim_{x \to 3} \frac{x - 3}{x^{2} - 9}$
1926	Evaluate the Limit	limit as x approaches -3 of f(x)	$lim_{x \to - 3} f (x)$
1927	Find the Local Maxima and Minima	f(x)=2x^3-3x^2-12x	$f (x) = 2 x^{3} - 3 x^{2} - 12 x$
1928	Find the Local Maxima and Minima	f(x)=3x^5-5x^3	$f (x) = 3 x^{5} - 5 x^{3}$
1929	Find the Local Maxima and Minima	f(x)=x^4-12x^3	$f (x) = x^{4} - 12 x^{3}$
1930	Find the Local Maxima and Minima	f(x)=x^3-3x+2	$f (x) = x^{3} - 3 x + 2$
1931	Find the Local Maxima and Minima	f(x)=xe^(-x^2)	$f (x) = x e^{- x^{2}}$
1932	Evaluate the Limit	limit as x approaches 64 of ( square root of x-8)/(x-64)	$lim_{x \to 64} \frac{\sqrt{x} - 8}{x - 64}$
1933	Find the Domain and Range	f(x)=(x-3)(x^2-6x-18)	$f (x) = (x - 3) (x^{2} - 6 x - 18)$
1934	Find the Derivative - d/d@VAR	f(x)=3 square root of x+5	$f (x) = 3 \sqrt{x + 5}$
1935	Find the Local Maxima and Minima	x^3-12x	$x^{3} - 12 x$
1936	Find the Antiderivative	5x	$5 x$
1937	Find the Function	g'(x)=3x^2-2x-4	$g' (x) = 3 x^{2} - 2 x - 4$
1938	Find the Antiderivative	1/( square root of x)	$\frac{1}{\sqrt{x}}$
1939	Evaluate the Limit	limit as x approaches 9 of (3- square root of x)/(9x-x^2)	$lim_{x \to 9} \frac{3 - \sqrt{x}}{9 x - x^{2}}$
1940	Evaluate the Limit	limit as x approaches infinity of square root of 49x^2+x-7x	$lim_{x \to \infty} \sqrt{49 x^{2} + x} - 7 x$
1941	Evaluate the Limit	limit as x approaches 0 of (1+x)^(8/x)	$lim_{x \to 0} {(1 + x)}^{\frac{8}{x}}$
1942	Evaluate the Limit	limit as x approaches 25 of (5- square root of x)/(25x-x^2)	$lim_{x \to 25} \frac{5 - \sqrt{x}}{25 x - x^{2}}$
1943	Evaluate the Limit	( limit as x approaches 16 of 4- square root of x)/(x-16)	$\frac{lim_{x \to 16} 4 - \sqrt{x}}{x - 16}$
1944	Evaluate the Limit	( limit as x approaches 1 of x^3-1)/(x-1)	$\frac{lim_{x \to 1} x^{3} - 1}{x - 1}$
1945	Evaluate the Limit	( limit as x approaches -1 of x^2-1)/(x+1)	$\frac{lim_{x \to - 1} x^{2} - 1}{x + 1}$
1946	Evaluate the Limit	( limit as x approaches -1 of x^2-4x)/(x^2-3x-4)	$\frac{lim_{x \to - 1} x^{2} - 4 x}{x^{2} - 3 x - 4}$
1947	Evaluate the Limit	( limit as x approaches 4 of x^3-64)/(x-4)	$\frac{lim_{x \to 4} x^{3} - 64}{x - 4}$
1948	Evaluate the Limit	( limit as x approaches 4 of x-4)/(x^2-16)	$\frac{lim_{x \to 4} x - 4}{x^{2} - 16}$
1949	Evaluate the Limit	( limit as x approaches 4 of x-4)/(x^2-3x-4)	$\frac{lim_{x \to 4} x - 4}{x^{2} - 3 x - 4}$
1950	Evaluate the Limit	( limit as x approaches -2 of x+2)/(x^3+8)	$\frac{lim_{x \to - 2} x + 2}{x^{3} + 8}$
1951	Evaluate the Limit	( limit as x approaches 5 of x^2-5x+6)/(x-5)	$\frac{lim_{x \to 5} x^{2} - 5 x + 6}{x - 5}$
1952	Evaluate the Limit	( limit as x approaches 9 of x-9)/( square root of x-3)	$\frac{lim_{x \to 9} x - 9}{\sqrt{x} - 3}$
1953	Evaluate the Limit	limit as x approaches 4 of (2- square root of x)/(4x-x^2)	$lim_{x \to 4} \frac{2 - \sqrt{x}}{4 x - x^{2}}$
1954	Evaluate the Limit	limit as x approaches 3 of x/(x-3)	$lim_{x \to 3} \frac{x}{x - 3}$
1955	Evaluate the Limit	limit as x approaches 0 of ( square root of 4+x-2)/x	$lim_{x \to 0} \frac{\sqrt{4 + x} - 2}{x}$
1956	Evaluate the Limit	limit as x approaches 1 of (x-1)/( square root of x-1)	$lim_{x \to 1} \frac{x - 1}{\sqrt{x} - 1}$
1957	Evaluate the Limit	limit as x approaches 1 of (x^4-1)/(x^3-1)	$lim_{x \to 1} \frac{x^{4} - 1}{x^{3} - 1}$
1958	Evaluate the Limit	limit as x approaches -6 of (2x+12)/(\|x+6\|)	$lim_{x \to - 6} \frac{2 x + 12}{\| x + 6 \|}$
1959	Evaluate the Limit	limit as x approaches -9 of (x^2-81)/(x+9)	$lim_{x \to - 9} \frac{x^{2} - 81}{x + 9}$
1960	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(2x^2-x)	$lim_{x \to 0} \frac{\sin (x)}{2 x^{2} - x}$
1961	Evaluate the Limit	limit as x approaches 0 of sin(x) natural log of x	$lim_{x \to 0} \sin (x) \ln (x)$
1962	Evaluate the Limit	limit as x approaches 4 of F(x)	$lim_{x \to 4} F (x)$
1963	Evaluate the Limit	limit as x approaches 0 of cot(x)	$lim_{x \to 0} \cot (x)$
1964	Evaluate the Limit	limit as x approaches 0 of 2	$lim_{x \to 0} 2$
1965	Evaluate the Limit	limit as x approaches 0 of x^2sin(1/x)	$lim_{x \to 0} x^{2} \sin (\frac{1}{x})$
1966	Evaluate the Limit	limit as x approaches 5 of (x-5)/(x^2-25)	$lim_{x \to 5} \frac{x - 5}{x^{2} - 25}$
1967	Evaluate the Limit	limit as x approaches 1 of x/( natural log of x)	$lim_{x \to 1} \frac{x}{\ln (x)}$
1968	Evaluate the Limit	limit as x approaches 1 of (2-x)/((x-1)^2)	$lim_{x \to 1} \frac{2 - x}{{(x - 1)}^{2}}$
1969	Evaluate the Limit	limit as x approaches 0 of ( square root of 2+x- square root of 2)/x	$lim_{x \to 0} \frac{\sqrt{2 + x} - \sqrt{2}}{x}$
1970	Evaluate the Limit	limit as x approaches -1 of 1/(x+1)	$lim_{x \to - 1} \frac{1}{x + 1}$
1971	Evaluate the Limit	limit as x approaches 1 of (1/x-1)/(x-1)	$lim_{x \to 1} \frac{\frac{1}{x} - 1}{x - 1}$
1972	Evaluate the Limit	limit as x approaches -2 of F(x)	$lim_{x \to - 2} F (x)$
1973	Evaluate the Limit	limit as t approaches infinity of ( square root of t+t^2)/(2t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{2 t - t^{2}}$
1974	Evaluate the Limit	limit as x approaches infinity of square root of 36x^2+x-6x	$lim_{x \to \infty} \sqrt{36 x^{2} + x} - 6 x$
1975	Evaluate the Limit	limit as x approaches 7 of (x^2-49)/(x-7)	$lim_{x \to 7} \frac{x^{2} - 49}{x - 7}$
1976	Evaluate the Limit	limit as x approaches infinity of square root of 81x^2+x-9x	$lim_{x \to \infty} \sqrt{81 x^{2} + x} - 9 x$
1977	Evaluate the Limit	limit as x approaches 5 of (x+1)/(x-5)	$lim_{x \to 5} \frac{x + 1}{x - 5}$
1978	Evaluate the Limit	limit as x approaches 1 of ( square root of x-x^2)/(1- square root of x)	$lim_{x \to 1} \frac{\sqrt{x} - x^{2}}{1 - \sqrt{x}}$
1979	Find the Area Between the Curves	y=x , y = fourth root of x	$y = x$ , $y = \sqrt[4]{x}$
1980	Find the Area Between the Curves	y=x+12 , y=x^2	$y = x + 12$ , $y = x^{2}$
1981	Find the Area Between the Curves	y=1/2x^2 , y=-x^2+6	$y = \frac{1}{2} x^{2}$ , $y = - x^{2} + 6$
1982	Find the Area Between the Curves	y=x^2+2x-4 , y=x+4	$y = x^{2} + 2 x - 4$ , $y = x + 4$
1983	Find the Area Between the Curves	y=x^2+9x-4 , y=x+2	$y = x^{2} + 9 x - 4$ , $y = x + 2$
1984	Find the Area Between the Curves	y=x^2-5x+4 , y=-(x-1)^2	$y = x^{2} - 5 x + 4$ , $y = - {(x - 1)}^{2}$
1985	Find the Tangent Line at the Point	y=x^2+6 , (1,7)	$y = x^{2} + 6$ , $(1, 7)$
1986	Evaluate the Limit	( limit as x approaches 0 of sin(x))/(5x)	$\frac{lim_{x \to 0} \sin (x)}{5 x}$
1987	Find the Tangent Line at the Point	y=x^3-3x , (2,2)	$y = x^{3} - 3 x$ , $(2, 2)$
1988	Evaluate the Limit	( limit as h approaches 0 of (4+h)^2-16)/h	$\frac{lim_{h \to 0} {(4 + h)}^{2} - 16}{h}$
1989	Graph	natural log of 8	$\ln (8)$
1990	Evaluate	natural log of infinity	$\ln (\infty)$
1991	Graph	natural log of tan(x)	$\ln (\tan (x))$
1992	Graph	natural log of 8x	$\ln (8 x)$
1993	Graph	natural log of cos(x)	$\ln (\cos (x))$
1994	Graph	natural log of 4x	$\ln (4 x)$
1995	Evaluate	2 natural log of 2	$2 \ln (2)$
1996	Solve for ?	tan(x)=-1/3	$\tan (x) = \frac{- 1}{3}$
1997	Solve for p	q=9000-100p	$q = 9000 - 100 p$
1998	Solve for r	144pr-6p^2r^2=0	$144 p r - 6 p^{2} r^{2} = 0$
1999	Solve for x	natural log of x^2-1=3	$\ln (x^{2} - 1) = 3$
2000	Solve for x	3x^2-2x-1=0	$3 x^{2} - 2 x - 1 = 0$