2.1-2.3 Quiz: Derivative and Power Rule PDF

2.1-2.3 Quiz: Definition of derivative and Power Rule ===================================================== +-----------------------------------+-----------------------------------+ | 7. Evaluate the limit: | 8. Evaluate the limit: | | [\$\\lim\_{h \\rightarrow | [...

2.1-2.3 Quiz: Definition of derivative and Power Rule ===================================================== +-----------------------------------+-----------------------------------+ | 7. Evaluate the limit: | 8. Evaluate the limit: | | [\$\\lim\_{h \\rightarrow | [\$\\lim\_{h \\rightarrow | | 0}\\frac{3\\sqrt{x + h} - | 0}\\frac{3\\sin\\left( x + h | | 3\\sqrt{x}}{h}\$]{.math | \\right) - 3sinx}{h}\$]{.math | |.inline} |.inline} | +===================================+===================================+ | 1. Evaluate the limit: | 2. Find | | [\$\\lim\_{h \\rightarrow | [\$\\frac{\\text{dy}}{\\text{ | | 0}\\frac{3\\left( x + h | dx}}:\\ | | \\right)\^{2} - 4\\left( x + | \\ y = 3x\^{5} - 2x\^{3} + | | h \\right) + 5 - (3x\^{2} - | 24\$]{.math.inline} | | 4x + 5)}{h}\$]{.math.inline} | | +-----------------------------------+-----------------------------------+ | 3. Find [\$f\^{\'}\\left( x | 4. Find the derivative of g(x). | | \\right):\\ \\ \\ f\\left( x | [*g*(*x*) = 3*x*^4^ + 4cos *x | | \\right) = \\ \\frac{x\^{3} - | *]{.math | | 3x}{\\sqrt{x}}\$]{.math |.inline} | |.inline} | | +-----------------------------------+-----------------------------------+ | 5. Find the instantaneous rate | 6. Find an equation for the | | of change of w if | tangent line to the graph of | | | | | w = | [\$f\\left( x \\right) = | | [\$\\frac{3}{4z\^{3}}\$]{.mat | 4x\^{4} + | | h | \\frac{1}{x\^{3}}\$]{.math | |.inline} |.inline} at the point where x | | | = 1. | +-----------------------------------+-----------------------------------+ Diagram Description automatically generated with low confidence