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The values of a and b so that the functi...

The values of a and b so that the function `f(x) = {{:(x + a sqrt(2) sin x",",0 le x lt pi//4),(2 x cot x + b",",pi//4 le x le pi//2),(a cos 2 x - b sin x",",pi//2 lt x le pi):}` is continuous for `x in [0, pi]`, are

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The correct Answer is:
a=(pi)/6,b=-(pi)/12`
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VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
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  4. Let R be the set of real numbers and f : R to R be such that for all x...

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

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

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

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

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  13. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

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  14. If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not diff...

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  15. Determine the values of x for which the following functions fails to b...

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  16. "If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1," prove...

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  17. Let alpha in R. Prove that a function f: RtoR is differentiable a...

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  18. Q. f={(x+a if x<0), (|x-1| if x>=0) g(x)={(x+1 if x<0),(x-1)^2 + b ...

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  19. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

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  20. If |cos^-1(1)/(n)|lt (pi)/(2), then lim(n to oo) {(n+1)(2)/(pi)cos^-...

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