Question

Let a function y = f(x) is defined by x = e^θsinθ and y = θe^sinθ, where θ is a real parameter, then value of `lim_(θ→0)`f'(x) is ______.

Options

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

Let a function y = f(x) is defined by x = e^θsinθ and y = θe^sinθ, where θ is a real parameter, then value of `lim_(θ→0)`f'(x) is 1.00.

Explanation:

f'(x) = `(dy)/(dx) = (e^sinθ(1 + θcosθ))/(e^θ(sinθ + cosθ))`

∴ `lim_(θ→θ)f^'(x) = lim_(θ→θ)(e^sinθ(1 + θcosθ))/(e^θ(sinθ + cosθ))` = 1