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Evaluate lim(xto0)(int(0)^(x^(2))cost^(2...

Evaluate `lim_(xto0)(int_(0)^(x^(2))cost^(2)dt)/(x sin x)`

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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Fill in the blanks so that the resulting statement is correct. Let f(x...

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  2. Let F(x)=f(x) g(x) h(x) for all real x, where f(x), g(x), and h(x) are...

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  3. Evaluate lim(xto0)(int(0)^(x^(2))cost^(2)dt)/(x sin x)

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  4. If (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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  5. If y={(log)(cosx)sinx}{(log)(sinx)cosx}^(-1)+sin^(-1)((2x)/(1+x^2)),fi...

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  6. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

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  7. Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le...

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  8. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  9. Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g...

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  10. Let f be a continuous, g be a discontinuous function. Prove that f + g...

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  11. Let f(x) be continuous function satisfying the condition f(-x) = f...

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  12. Let R be the set of real numbers and f : R to R be such that for all x...

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  13. The points where the function f(x) = [x] + |1 - x|, -1 < x < 3 where [...

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  14. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

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  15. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

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  16. A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y...

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  17. Given that f(x)= {((1-cos4x)/(x^(2))",","if "x lt 0),(a",","if "x =0),...

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  18. Find (dy)/(dx) at x=-1, when (siny)^(sin.(pix)/(2))+(sqrt3)/(2)sec^(-1...

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  19. Find ("lim")(xvec0){tan(pi/4+x)}^(1//x)

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  20. Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x...

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