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< 2\…

If \(5^x + 5^y = 5^{x + y}\) then prove that \(\dfrac{dy}{dx} + 5^{y - x} = 0\). Differentiating with respect to …