Inverse Trigonometry Continuity and Differentiability

Differentiate the following w.r.t. x:

If log (x² + y²) If

Determine the values of a, b, and c for which the function

If

continuous at x = 2, find the value of k.

Differentiate the following w.r.t.x.

If

If x¹⁶y⁹ = (x²+ y)¹⁷ prove that

Verify Rolle’s Theorem for the function f, given by f(x) = e^x (sinx – cos x) on 

If

Find the values of k so that the function f is continuous at the indicated point 

Differentiate the functions:

Show that the function f=(x)=|x-3|, x ϵ R, is continuous but not differentiable at x = 3.

If y = Ae^mx + Be^nx, show that

Find all the points of discontinuity of the function f(x) = [x²] on [1, 2), where [.] denotes the greatest integer function.

If y = log tan (π/4 + x/2), show that dy/dx= sec. Also find the value of d²y/dx² at x = π/4.

Let f

Determine the value of ‘a’, if possible, so that the function is continuous at x = 0.

If

If

Differentiate

Find the relationship between a and b so that the function  f defined by