Popular Calculus Questions

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∫ln(1+tanx) from o to pi/4 1)pi*ln2/8 2)pi*ln2/4 3)pi*ln2 4)pi*ln4 ...

if α is the only root of the eqn x3+bx2+cx+1=0(b<c),then the vlaue of tan-1(α) + tan-1(α-1) a)-π/2 b)π/2 c)0 d)none ...

∫(x2/(xsinx+cosx)2)dx pls give some hints..... ...

let the fn f satisfy f(x).f'(-x)=f(-x)f'(x) for all x n f(o)=3 q1the value f(x)f(-x) for all x is a]4 b]9 c]12 d]16 q2 ∫dx/(3+f(x))[limit -51 to 51] a)17 b)34 c)102 d)0 q3 no of roots of f(x)=0 in[-2,2] a1 b0 c2 d4 ...

Let f be twice diff function satisfying f(1)=1,f(2)=4,f(3)=9 then: a)f"(x)=2 b)f'(x)=2 c)there exists at least one x E (1,3) such that f ' (x)=2 ...

Statement 1 *Image* Stat2 *Image* ...

Like the title says, this is not JEE stuff, but if you have been following some of my recent posts, this may be worthwhile doing: \int_0^1 f(x) \ dx = \int_0^1 x f(x) \ dx = 1 Prove that \int_0^1 f^2(x) \ dx \ge 4 ...

∫1/(x2(x4+1)) ...

\begin{vmatrix} 3x &4x &-5 \\ 2x^{2}&9 &2x \\ x& 8 & 3x \end{vmatrix} = ax^{4}+ bx^{3}+cx^{2}+ dx+e, then, the value of 6a+5b+4c+3d+2e is equal to....... a.273 b.235 c.-15 d.-53 ...

Find the limit to: *Image* the options are: A.)(a-b)/3 B.)0 C.)(a2-b2)/6a2b2 D.)(a2-b2)/3a2b2 ...

\int_{4}^{x}{t^{2}-8t+16dt} on [0,5] is: ...

Can anyone prove that sin-1x=-cos-1x + c I forgot the c ...

\int_{0}^{10}f(x)dx{} then\sum_{k=1}^{10}{\int f((k-1)+x)dx}=?? ...

Q) A window is in the shape of a rectangle surmounted by a semicircle,If the Perimetre of the Window is Pcm show that the Window lest in the maximum possible light only when the radius of the semicircle is P/(Ï€+4)cm.? Prove ...

Let f be a differentiable function such that f(x+y)=f(x)+f(y)+x2y and lim f(x) = 0 x→0 x Then find f'(10) ...

integrate [ a+c] to [b+c] f(x)dx ...

1. xsinx dx 1+cos2x 2. (x-1)(x-2)(x-3 dx ...

Q3 lim x->infinity [(x+p)(x+q)(x+r)(x+s)]^1/4 - x x SOLN. ([(x+p)(x+q)(x+r)(x+s)] - x4)/([(x+p)(x+q)(x+r)(x+s)]1/4 + x)([(x+p)(x+q)(x+r)(x+s)]1/2 + x2) now divide numerator and deno by x3 this was a soln by NIshant Sir, Si ...

the question is x2-√x/(√x)-x limit x tending to 1 plz solve this both by dirct derivative and 1st priciple 2)√tanx solve this by 1st principle ...

THIS ONE IS FRM DA FORUM ITSELF : If f(x) f'(x) f"(x)>0 for all x in R, prove that f(x) is a strictly increasing function CAN NE1 PLZZZ XPLAIN ME THIS EXPLANATION OF CELESTINE f'x never 0 , so either strict inc or strict d ...

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*Image* plz solve............... ...

If 0∫x f(t)dt = x + x∫1 t f(t)dt , Find f(1). I am getting two answers for this!! Pls. try it & explain!! ...

WHAT ARE NON INTEGRABLE FUNCTIONS? GIVE EXAMPLES. ...

how to draw the graph {x} and please help me to draw the graph y={x}2 and {x}={y} ...

Find all the values of parameters a(a≥1) for which the areaa of figure bounded by pair of straight lines y2-3y+2=0 and curves y=[a]x2 ,y=[a]x2/2 is greatest..... where [ ] is GINT ...

Find the Integer N such that (N+1)2=(N)2+(N-1)2 ...

*Image* The diagram shows the graph of the derivative of a function y=f(x) for 0<=x<=5 with f(0)=0. ∫f(x)dx= [limits from 0 to 1] a.-21/20 b.21/20 c.-1 d.none of these Sir u said option b or d must be correct out of d ...

f(x)=ax3+bx2+cx+dsin x. Findthe condition that f(x) is always injective function. 2. Let f: X→Y be a function defined by f(x)= a sin(x+pi/4)+b cos x+c.If f(x) is bijective,find X. ...