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GO Classes 2025 | Weekly Quiz 21 | Calculus | Question: 15

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Find the values of $A$ and $B$ that make
$$
f(x)=\left\{\begin{array}{lll}
x^2+1 & \text { if } & x \geq 0 \\
A \sin x+B \cos x & \text { if } & x<0
\end{array}\right.
$$
differentiable at $x=0$.

  1. $A=0, B=1$
  2. $A=1, B=0$
  3. $A=0, B=-1$
  4. $A=-1, B=0$
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f(x) is differentiable at x=0 → f(x) is continuous at x=0

So, $\lim_{x→0^{+}}$ f(x) = $\lim_{x→0^{-}}$ f(x) = f(0)

=> $\lim_{x→0^{-}}$ f(x) = f(0)

=> A sin(0) + B cos(0) = 0$^{2}$ + 1

=> B = 1
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