Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2901	Evaluate the Limit	limit as x approaches 9 of (x^2-81)/(x-9)	$lim_{x \to 9} \frac{x^{2} - 81}{x - 9}$
2902	Evaluate the Limit	limit as x approaches negative infinity of x^6+x^7	$lim_{x \to - \infty} x^{6} + x^{7}$
2903	Evaluate the Limit	limit as x approaches infinity of ( square root of x+x^2)/(2x-x^2)	$lim_{x \to \infty} \frac{\sqrt{x} + x^{2}}{2 x - x^{2}}$
2904	Evaluate the Limit	limit as x approaches 144 of ( square root of x-12)/(x-144)	$lim_{x \to 144} \frac{\sqrt{x} - 12}{x - 144}$
2905	Evaluate the Limit	limit as x approaches -7 of (x^2-49)/(x+7)	$lim_{x \to - 7} \frac{x^{2} - 49}{x + 7}$
2906	Evaluate the Limit	limit as x approaches infinity of (5x^3+1)/(x-x^3)	$lim_{x \to \infty} \frac{5 x^{3} + 1}{x - x^{3}}$
2907	Evaluate the Limit	limit as x approaches 3 of natural log of x-3	$lim_{x \to 3} \ln (x - 3)$
2908	Find the Derivative - d/dx	x^12e^x	$x^{12} e^{x}$
2909	Evaluate the Limit	limit as h approaches 0 of ( square root of 25+h-5)/h	$lim_{h \to 0} \frac{\sqrt{25 + h} - 5}{h}$
2910	Evaluate the Limit	limit as t approaches infinity of ( square root of t+t^2)/(3t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{3 t - t^{2}}$
2911	Evaluate the Limit	limit as h approaches 0 of ( square root of 16+h-4)/h	$lim_{h \to 0} \frac{\sqrt{16 + h} - 4}{h}$
2912	Evaluate the Limit	limit as x approaches infinity of ( square root of x+x^2)/(5x-x^2)	$lim_{x \to \infty} \frac{\sqrt{x} + x^{2}}{5 x - x^{2}}$
2913	Evaluate the Limit	limit as x approaches 5 of 12	$lim_{x \to 5} 12$
2914	Evaluate the Limit	limit as x approaches -1 of (2x^2-x-3)/(x+1)	$lim_{x \to - 1} \frac{2 x^{2} - x - 3}{x + 1}$
2915	Evaluate the Limit	limit as x approaches 4 of g(x)	$lim_{x \to 4} g (x)$
2916	Find the Derivative - d/dx	a^9+cos(x)^9	$a^{9} + \cos^{9} (x)$
2917	Find the Local Maxima and Minima	f(x)=2x^3-3x^2-36x	$f (x) = 2 x^{3} - 3 x^{2} - 36 x$
2918	Find the Local Maxima and Minima	f(x)=4x^3-12x	$f (x) = 4 x^{3} - 12 x$
2919	Find the Local Maxima and Minima	f(x)=5x^3-15x	$f (x) = 5 x^{3} - 15 x$
2920	Find the Derivative - d/dx	y = cube root of 6x^2+1	$y = \sqrt[3]{6 x^{2} + 1}$
2921	Find the Local Maxima and Minima	f(x)=x^3-6x^2	$f (x) = x^{3} - 6 x^{2}$
2922	Find the Local Maxima and Minima	f(x)=x^5 natural log of x	$f (x) = x^{5} \ln (x)$
2923	Find the Local Maxima and Minima	f(x)=x^2 natural log of x	$f (x) = x^{2} \ln (x)$
2924	Find the Local Maxima and Minima	f(x)=x^2-4x+7	$f (x) = x^{2} - 4 x + 7$
2925	Find the Local Maxima and Minima	f(x)=x^2+4x+5	$f (x) = x^{2} + 4 x + 5$
2926	Find dy/dx	y=(x+7)(x^2-7)	$y = (x + 7) (x^{2} - 7)$
2927	Find the Local Maxima and Minima	f(x)=x^3-3x^2+3	$f (x) = x^{3} - 3 x^{2} + 3$
2928	Find the Derivative - d/dx	y=(7 square root of x)/8	$y = \frac{7 \sqrt{x}}{8}$
2929	Find the Local Maxima and Minima	y=x^4-2x^2	$y = x^{4} - 2 x^{2}$
2930	Find the Local Maxima and Minima	y=(x^2-5)/(x-3)	$y = \frac{x^{2} - 5}{x - 3}$
2931	Find the Derivative - d/dx	7x^3	$7 x^{3}$
2932	Find the Local Maxima and Minima	f(x)=x+2cos(x)	$f (x) = x + 2 \cos (x)$
2933	Find the Local Maxima and Minima	f(x)=cos(pix)	$f (x) = \cos (π x)$
2934	Find the Local Maxima and Minima	f(x) = natural log of x^4+27	$f (x) = \ln (x^{4} + 27)$
2935	Find the Derivative - d/d@VAR	f(x)=-sin(x)	$f (x) = - \sin (x)$
2936	Find the Derivative - d/d@VAR	f(x)=sin( natural log of x)	$f (x) = \sin (\ln (x))$
2937	Find the Derivative - d/d@VAR	f(x)=sin(pix)	$f (x) = \sin (π x)$
2938	Find the Derivative - d/d@VAR	F(x)=(4x+1)^2	$F (x) = {(4 x + 1)}^{2}$
2939	Find the Derivative - d/d@VAR	f(x)=x^2+4	$f (x) = x^{2} + 4$
2940	Find the Derivative - d/d@VAR	f(x)=5e^x	$f (x) = 5 e^{x}$
2941	Find the Derivative - d/d@VAR	f(x)=2x^4	$f (x) = 2 x^{4}$
2942	Find the Derivative - d/d@VAR	f(x)=6x^3	$f (x) = 6 x^{3}$
2943	Find the Derivative - d/d@VAR	f(x) = square root of 2-6x	$f (x) = \sqrt{2 - 6 x}$
2944	Find the Derivative - d/d@VAR	f(x)=2e^(3x-1)	$f (x) = 2 e^{3 x - 1}$
2945	Find the Derivative - d/d@VAR	f(x)=x^2+x-5	$f (x) = x^{2} + x - 5$
2946	Find the Derivative - d/dx	square root of 7x+ square root of 7x+ square root of 7x	$\sqrt{7 x + \sqrt{7 x + \sqrt{7 x}}}$
2947	Find the Local Maxima and Minima	f(x)=(x^2-1)^3	$f (x) = {(x^{2} - 1)}^{3}$
2948	Find the Local Maxima and Minima	x^3-12x+2	$x^{3} - 12 x + 2$
2949	Find the Antiderivative	-x^2	$- x^{2}$
2950	Find the Antiderivative	\|x\|	$\| x \|$
2951	Find the Antiderivative	2/x	$\frac{2}{x}$
2952	Find the Antiderivative	arctan(x)	$\arctan (x)$
2953	Find the Antiderivative	3x^3	$3 x^{3}$
2954	Find the Antiderivative	5x^2	$5 x^{2}$
2955	Find the Antiderivative	f(x)=e^(2x)	$f (x) = e^{2 x}$
2956	Find the Antiderivative	f(x)=x^(1/3)	$f (x) = x^{\frac{1}{3}}$
2957	Find the Antiderivative	f(x)=1/2x^2-2x+6	$f (x) = \frac{1}{2} x^{2} - 2 x + 6$
2958	Find the Antiderivative	f(x)=x(2-x)^2	$f (x) = x {(2 - x)}^{2}$
2959	Find the Antiderivative	f(x)=18x^5	$f (x) = 18 x^{5}$
2960	Find the Antiderivative	f(x)=144-x^2	$f (x) = 144 - x^{2}$
2961	Find the Antiderivative	f(x)=3x	$f (x) = 3 x$
2962	Find dy/dx	y=(2x+1)^(4x)	$y = {(2 x + 1)}^{4 x}$
2963	Find the Difference Quotient	f(x)=5x^2	$f (x) = 5 x^{2}$
2964	Find the Derivative - d/dx	e^x-cot(x)	$e^{x} - \cot (x)$
2965	Evaluate the Limit	limit as h approaches 0 of ((x+h)^2-x^2)/h	$lim_{h \to 0} \frac{{(x + h)}^{2} - x^{2}}{h}$
2966	Evaluate the Limit	limit as h approaches 0 of h+2x+1	$lim_{h \to 0} h + 2 x + 1$
2967	Evaluate the Limit	limit as x approaches infinity of f(x)+2g(x)	$lim_{x \to \infty} f (x) + 2 g (x)$
2968	Evaluate the Limit	limit as t approaches 0 of 5/(t square root of 1+t)-5/t	$lim_{t \to 0} \frac{5}{t \sqrt{1 + t}} - \frac{5}{t}$
2969	Evaluate the Limit	( limit as x approaches 2 of x^2-5x+6)/(x-2)	$\frac{lim_{x \to 2} x^{2} - 5 x + 6}{x - 2}$
2970	Evaluate the Limit	limit as x approaches 0 of 1/x-1/(x^2+x)	$lim_{x \to 0} \frac{1}{x} - \frac{1}{x^{2} + x}$
2971	Evaluate the Limit	( limit as x approaches 2 of square root of x+2-2)/(x-2)	$\frac{lim_{x \to 2} \sqrt{x + 2} - 2}{x - 2}$
2972	Evaluate the Limit	( limit as x approaches 16 of 4- square root of x)/(16x-x^2)	$\frac{lim_{x \to 16} 4 - \sqrt{x}}{16 x - x^{2}}$
2973	Evaluate the Limit	( limit as x approaches 1 of x-1)/( square root of x-1)	$\frac{lim_{x \to 1} x - 1}{\sqrt{x} - 1}$
2974	Evaluate the Limit	( limit as x approaches 100 of square root of x-10)/(x-100)	$\frac{lim_{x \to 100} \sqrt{x} - 10}{x - 100}$
2975	Evaluate the Limit	( limit as x approaches -2 of \|x+2\|)/(x+2)	$\frac{lim_{x \to - 2} \| x + 2 \|}{x + 2}$
2976	Evaluate the Limit	( limit as x approaches 2 of 1/x-1/2)/(x-2)	$\frac{lim_{x \to 2} \frac{1}{x} - \frac{1}{2}}{x - 2}$
2977	Evaluate the Limit	( limit as x approaches -1 of 2x^2-x-3)/(x+1)	$\frac{lim_{x \to - 1} 2 x^{2} - x - 3}{x + 1}$
2978	Evaluate the Limit	( limit as x approaches -1 of 6x+5)/(5x-6)	$\frac{lim_{x \to - 1} 6 x + 5}{5 x - 6}$
2979	Evaluate the Limit	( limit as x approaches -4 of 1/4+1/x)/(4+x)	$\frac{lim_{x \to - 4} \frac{1}{4} + \frac{1}{x}}{4 + x}$
2980	Evaluate the Limit	( limit as x approaches 3 of x^3-27)/(x^2-9)	$\frac{lim_{x \to 3} x^{3} - 27}{x^{2} - 9}$
2981	Evaluate the Limit	( limit as x approaches 3 of x^3-27)/(x-3)	$\frac{lim_{x \to 3} x^{3} - 27}{x - 3}$
2982	Evaluate the Limit	( limit as x approaches 3 of x^3-9x)/(x-3)	$\frac{lim_{x \to 3} x^{3} - 9 x}{x - 3}$
2983	Evaluate the Limit	( limit as x approaches -3 of x^2+x-6)/(x^2-9)	$\frac{lim_{x \to - 3} x^{2} + x - 6}{x^{2} - 9}$
2984	Evaluate the Limit	( limit as x approaches 2 of x^5-32)/(x-2)	$\frac{lim_{x \to 2} x^{5} - 32}{x - 2}$
2985	Evaluate the Limit	( limit as x approaches 2 of x-3)/(x-2)	$\frac{lim_{x \to 2} x - 3}{x - 2}$
2986	Evaluate the Limit	limit as x approaches 5 of (x^3-125)/(x-5)	$lim_{x \to 5} \frac{x^{3} - 125}{x - 5}$
2987	Evaluate the Limit	( limit as x approaches 5 of x^3-125)/(x-5)	$\frac{lim_{x \to 5} x^{3} - 125}{x - 5}$
2988	Evaluate the Limit	( limit as x approaches 8 of cube root of x-2)/(x-8)	$\frac{lim_{x \to 8} \sqrt[3]{x} - 2}{x - 8}$
2989	Evaluate the Limit	( limit as x approaches 9 of 9-x)/( square root of x-3)	$\frac{lim_{x \to 9} 9 - x}{\sqrt{x} - 3}$
2990	Evaluate the Limit	( limit as x approaches a of x^2-a^2)/(x-a)	$\frac{lim_{x \to a} x^{2} - a^{2}}{x - a}$
2991	Evaluate the Limit	limit as x approaches 0 of (2^x-1)/x	$lim_{x \to 0} \frac{2^{x} - 1}{x}$
2992	Evaluate the Limit	limit as x approaches 0 of (1-8x)^(1/x)	$lim_{x \to 0} {(1 - 8 x)}^{\frac{1}{x}}$
2993	Evaluate the Limit	limit as x approaches 0 of (x^2-x)/x	$lim_{x \to 0} \frac{x^{2} - x}{x}$
2994	Evaluate the Limit	limit as x approaches 0 of 2sin(x)-1	$lim_{x \to 0} 2 \sin (x) - 1$
2995	Evaluate the Limit	limit as h approaches 0 of (f(x+h)-f(x))/h	$lim_{h \to 0} \frac{f (x + h) - f (x)}{h}$
2996	Evaluate the Limit	limit as h approaches 0 of ( square root of 36+h-6)/h	$lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}$
2997	Evaluate the Limit	limit as x approaches 0 of (sin(2x))/(sin(5x))	$lim_{x \to 0} \frac{\sin (2 x)}{\sin (5 x)}$
2998	Evaluate the Limit	limit as x approaches 0 of (sin(5x))/(sin(2x))	$lim_{x \to 0} \frac{\sin (5 x)}{\sin (2 x)}$
2999	Evaluate the Limit	limit as x approaches 4 of (x^2+3x-28)/(x^2-16)	$lim_{x \to 4} \frac{x^{2} + 3 x - 28}{x^{2} - 16}$
3000	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(\|x\|)	$lim_{x \to 0} \frac{\sin (x)}{\| x \|}$