If `f(x)=|sinx-|cosx||,` then the value of `f^'(x)` at `x=(7pi)/6` is
(a) `positive` (b) `(1-sqrt(3))/2` (c)`0` (d) none of these

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(pi)/2 (b) (pi)/2-11 (c) (5pi)/2-11 (d) none of these

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^('')dx+int_1^3f^('')dx is equal to -1/(sqrt(3)) (b) 1/(sqrt(3)) (e) 0 (d) none of these

If f(x)=sqrt(x^2-10 x+25) , then the derivative of f(x) in the interval [0, 7] is (a) 1 (b) -1 (c) 0 (d) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a) [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

If 2f(x)-3f(1/x)=x^2(x!=0), then f(2) is equal to (a) -7/4("b")""5/2 (c) -1 (d) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is (a)[0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The value of int_0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(sin x))dx is pi//2 b. pi//4 c. 0 d. none of these

If f(x)=|cosx-sinx| , find f^(prime)(pi/6) and f^(prime)(pi/3) .

If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , then the value of k is (a) 0 (b) 1 (c) -1 (d) None of these