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For Numbers $46$ - $50$: MULTIPLE-CHOICE$\newline$INSTRUCTIONS: A if ONLY the FIRST statement is ALWAYS true, B if ONLY the SECOND statement is ALWAYS true, $\mathbf{C}$ if BOTH STATEMENTS are ALWAYS true and D if BOTH STATEMENTS are NOT always true.$\newline$$46$. Functions expressed in the form of $\mathrm{y}=\mathrm{f}(\mathrm{x})$ can be solely differentiated explicitly. However, curves that fail both the vertical line test and the horizontal line test are not differentiable.$\newline$$47$. In differentiating a function with respect to its independent variable, you take the derivative as it is (for example the derivative of $\mathrm{y}^{2}$ with respect to $\mathrm{x}$ is $2 \mathrm{y}$ ) but you add it with the factor of the inner function's derivative (dy/dx), as encapsulated by the chain rule.$\newline$The $\mathrm{dy} / \mathrm{dx}$ is always a unique value, meaning the value of the slope never repeats for all $(x, y)$ that lie on a given curve.$\newline$$48$. If $f(x)=g(x)$, then $f_{0}(x)=g_{0}(x)$. If $f_{0}(x)=g_{0}(x)$, then $f(x)=g(x)$.$\newline$$49$. If a function is integrable over the interval $\mathrm{y}=\mathrm{f}(\mathrm{x})$$1$, then it is continuous.$\newline$Conversely, continuity implies integrability.$\newline$$50$. Differentiability (over an interval) implies integrability.$\newline$If a function is integrable over an interval, then it is differentiable for all points between the endpoints of that interval.