How to Find Horizontal Asymptotes of a Rational Function? The rational function is defined as: \(f(x)=\dfrac{P(x)}{Q(…

Question: Evaluate the derivative of $|x-3|$ at $x=-1$ Answer: Writing the function in piecewise form, we g…

Question: For what value of $x$, $f(x)=|2x-7|$ is not differentiable. Answer: We need to find the input …

Question: Consider \[f(x)=\left\{\begin{array}{ll} \frac{x^{2}-x-6}{x+2} & x \neq-2 \ -5 & x=-2 \e…

Question: For what value of $k$,\[ f(x) =\left\{ \begin{array}{ll} 4x^2-kx-10 & 0 \leq x Answe…

If $5^x+5^y=5^{x+y}$ then prove that ${\displaystyle \frac{dy}{dx}}+5^{y-x}=0$. Differentiating with respect to …