Question

f(x)=x sin5x÷tan2x. tan7x. f(0)=5÷9 then at x=0 f( x)

Answer 1

Answer:here's your answer  

Step-by-step explanation:56777

Answer 2

f(x)=x sin5x÷tan2x. tan7x. f(0)=5÷9 then at x=0 f( x)

Given,

$f(x) = \dfrac{xsin5x}{tan2x \times tan7x}$

$f(0) = \lim_{x \to 0} f(x)$

$\Rightarrow \lim_{x\to 0} \dfrac{xsin5x}{tan2x \times tan 7x}$

$\lim_{x\to 0} \dfrac{\frac{sin5x}{5x}x(5x)x}{\frac{tan2x}{2x}(2x) \times \frac{tan7x}{7x}(7x)}$

$\lim_{x\to 0} \dfrac{5x^2}{14x^2}\times \dfrac{sin5x}{5x} \times \dfrac{1}{\frac{tan2x}{2x} \times \frac{tan7x}{7x}}$

$= \dfrac{5}{14} \times 1 \times \dfrac{1}{1 \times 1}$

f(0) = 5 / 14

Given, f(0) = 5 / 9

Therefore f(x) is discontinuous.