Question

Limit x tends to 0 (x^2+5x/x^3+x)

Answer 1

Solution:-

$\lim_{x \to 0} \dfrac{x^{2}+5x }{x^{3}+x}$

Now put the value of x = o

=>  $\dfrac{x^{2}+5x }{x^{3}+x } = \dfrac{0+0}{0+0} =\dfrac{0}{0}\:\: form$

Now factorise the form

⇒$\lim_{x \to 0}\dfrac{x(x+5)}{x(x^{2}+1) }$

⇒$\lim_{x \to 0}\dfrac{\cancel{x} (x+5)}{\cancel{x}(x^{2}+1) }$

⇒$\lim_{x \to 0}\dfrac{ (x+5)}{(x^{2}+1) }$

⇒$\lim_{x \to 0} \dfrac{x^{2}+5x }{x^{3} +x}$

put the value of x = 0

⇒$\dfrac{0+5}{0+1} =5$

Answer=5