(Solved): Application - Linearization: Problem 1 (1 point) Given that \( f(5)=-3 \) and \( f^{\prime}(5)=-3 \ ...

Application - Linearization: Problem 1 (1 point) Given that \( f(5)=-3 \) and \( f^{\prime}(5)=-3 \), find an equation for the tangent line to the graph of \( y=f(x) \) at \( z=5 \). Find the local linearization of \( f(x)=x^{2} \) at 1 . \[ l_{1}(x)= \] Application - Linearization: Problem 3 (1 point) Find the linearization \( L(x) \) of the function at \( a \). \[ f(x)=\sqrt[3]{x}, \quad a=-8 \] \[ L(x)= \] Application - Linearization: Problem 4 (1 point) \( y=(2+x)^{-1 / 2}, \quad a=2 \) Find the Linearization at \( x=a \). \( L(x)= \) Find the linearization \( L(x) \) of \( y=\left(25+4 x^{2}\right)^{-1 / 2} \) at \( a=0 \). \[ L(x)= \] Find a linear approximation of the function \( f(x)=\sqrt[3]{1-x} \) at \( a=0 \) \[ \sqrt[3]{1-x} \approx \] Find the local linear approximation of the function \( f(x)=\sqrt{4+x} \) at \( x_{0}=5 \), and use it to approximate \( \sqrt{8.9} \) and \( \sqrt{9.1} \). (a) \( f(x)=\sqrt{4+x} \approx \) (b) \( \sqrt{8.9} \approx \) (c) \( \sqrt{9.1} \approx \) For parts (b) and (c). you should enter your onswer as a fraction. If you enter a decimat make sure that it is correct to at least six decimal places