Recently Active Calculus Questions

The inverse of the function f(x)=frac{{{e}^{x}}-{{e}^{-x}}}{{{e}^{x}}+{e}^{-x}}}+2 is given by a) {{log }_{e}}{{left( frac{x-2}{x-1} ight)}^{frac{1}{2}}} b) {{log }_{e}}{{left( frac{x-1}{3-x} ight)}^{frac{1}{2}}} c) {{log }_{ ...

If f :N→N such that f(f(x))=3x; Then find f(2013) ...

Let R = {(1, 3), (2, 2), (3, 2)} and S = {(2, 1), (3, 2), (2, 3)} be two relations on set A = {1, 2, 3}. Then RoS = a) {(1, 3), (2, 2), (3, 2), (2, 1), (2, 3)} b) {(3, 2), (1, 3)} c) {(2, 3), (3, 2), (2, 2)} d) {(2, 3), (3, 2 ...

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3 . Then {R^{ - 1}} is a) {(8, 11), (10, 13)} b) {(11, 18), (13, 10)} c) {(10, 13), (8, 11)} d) None of these ...

If varphi (x) = {a^x}, then {{ varphi (p)} ^3} is equal to a) phi(3p) b) 3varphi (p) c) 6phi(p) d) 2phi(p) ...

If then f(x),f(y) - frac{1}{2}[fleft({frac{x}{y}} ight) + f(xy)] = a) frac{1}{2} b) 2 c) 0 d) 1 ...

Let f(x)=(1+{{b}^{2}}){{x}^{2}}+2bx+1 and m(b) the minimum value of f(x) for a given b. As b varies, the range of m(b) is a) [0,,1] b) left( 0,left. frac{1}{2} ight] ight. c) left[ frac{1}{2},,,1 ight] d) (0,,1] ...

f(x)=cos sqrt{x}, correct statement is a) f(x) is periodic & its period =sqrt{2}pi b) f(x) is periodic & its period =4{{pi }^{2}} c) f(x) is periodic & its period =sqrt{pi } d) f(x) is not periodic ...

Lim Sin.Log x2 x→0 Find the value using L hospital rule. ...

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How to understand which variable is a function of which other variable. For eg:- In the formula : h = ut - (1/2)g(t^2) the variable h is a function of t How to make similar interpretations in case of other formulas? Can anyon ...

∫ cos 5x+ cos 4x/1-2cos3x ...

integrate 1/1+x^4 ...

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If x is a +ve number then , ∫ xπ /x-1 dx ...

Which of the following represents the same graph as {x}={y} a) tan(πy)=tan(πx) b) sin(πy)=sin(πx) c) cos(πy)=cos(πx) d) None of these ...

∫ x2/x4+x2-2 dx ...

show that ------- Lt (2+x)sin(2+x) - 2sin2 /x = 2cos2 + 2sin2 x→ 0 ...

calcullate : Lt asinx-xsina /ax2-ax2x x→a. ...

∫ sin(n+ 1/2 )x/sinx .dx. Integration from 0 to π. n is a natural number. ...

f(x) is defined for x > −1 and has a continuous derivate. If f satisfies f(0) = 1, f′(0) = 0; (1 + f(x)) f′′(x) = 1 + x. If x is positive then f′(x) is (A) always positive (B) always negative (C) always non-negat ...

tan-1(2x+1/(1-4x)) ...

find dy/dx if- y=sin2(cot-1(√(1+x)/√(1-x)) ...

tan-1((√(1+x)-√(1-x))/(√(1+x)+√(1-x))) ...

if g(x)=-√(25-x2) then Lt (g(x)-g(1))/x-1 =? x→1 ...

If f:R o R,,f(x)=2x-1 and g:R o R, g(x)={{x}^{2}} then (gof),(x) equals ...

The period of the function f(x)=2cos frac{1}{3}(x-pi ) is ...