$$\lim_{x\rightarrow7}\ \frac{\frac{1}{\sqrt[]{x^2-2x}}-\frac{1}{\sqrt[]{35}}}{x-7}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

Function: $$f\left(x\right)=\frac{1}{\sqrt[]{x^2}-2x}$$ Instantaneous rate at $$x=7$$

Function: $$f\left(x\right)=2x^2-6x+2$$ Instantaneous rate at $$x=4$$

Function: $$f\left(x\right)=1x^2-4x+2$$ Instantaneous rate at $$x=7$$

Function: $$f\left(x\right)=3x^2-7x+1$$ Instantaneous rate at $$x=3$$

$$\lim_{x\rightarrow-2}\ \frac{\left(3x-9x^2\right)+\left(42\right)}{x+2}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

Function: $$f\left(x\right)=3x-9x^2$$ Instantaneous rate at $$x=-2$$

Function: $$f\left(x\right)=2x-4x^2$$ Instantaneous rate at $$x=-2$$

Function: $$f\left(x\right)=5x-4x^2$$ Instantaneous rate at $$x=-1$$

Function: $$f\left(x\right)=6x-3x^2$$ Instantaneous rate at $$x=-1$$

$$\lim_{x\rightarrow0}\ \frac{3\ln\left(2+h\right)-3\ln2}{h}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

Function: $$f\left(x\right)=3\ln x$$ Instantaneous rate at: $$x=2$$

Function: $$f\left(x\right)=1\ln x$$ Instantaneous rate at: $$x=5$$

Function: $$f\left(x\right)=6\ln x$$ Instantaneous rate at: $$x=1$$

Function: $$f\left(x\right)=4\ln x$$ Instantaneous rate at: $$x=3$$

$$\lim_{h\rightarrow0}\ \frac{3\left(1+h\right)^2-7\left(1+h\right)+1+\left(3\right)}{h}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

Function: $$f\left(x\right)=3x^2-7x+1$$ Instantaneous rate at: $$x=1$$

Function: $$f\left(x\right)=7x^2-4x+3$$ Instantaneous rate at: $$x=8$$

Function: $$f\left(x\right)=5x^2-8x+1$$ Instantaneous rate at: $$x=2$$

Function: $$f\left(x\right)=1x^2-3x+2$$ Instantaneous rate at: $$x=3$$

$$\lim_{x\rightarrow\frac{\pi}{2}}\ \frac{6x^2\sin x-\frac{3\pi^2}{2}}{x-\frac{\pi}{2}}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

Function: $$f\left(x\right)=6x^2\sin x$$ Instantaneous rate at: $$x=\frac{\pi}{2}$$

Function: $$f\left(x\right)=3x^2\sin x$$ Instantaneous rate at: $$x=\frac{\pi}{3}$$

Function: $$f\left(x\right)=4x^2\sin x$$ Instantaneous rate at: $$x=3$$

Function: $$f\left(x\right)=7x^2\sin x$$ Instantaneous rate at: $$x=5$$

$$\lim_{h\rightarrow0}\ \frac{\log\left(2-4\left(h-5\right)\right)-\log\left(22\right)}{h}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

$$f\left(x\right)=\log\left(2-4x\right)$$ Instantaneous rate at: $$x=-5$$

$$f\left(x\right)=\log\left(3-1x\right)$$ Instantaneous rate at: $$x=-5$$

$$f\left(x\right)=\log\left(4-3x\right)$$ Instantaneous rate at: $$x=-2$$

$$f\left(x\right)=\log\left(6-4x\right)$$ Instantaneous rate at: $$x=-1$$

$$\lim_{x\rightarrow5}\frac{\frac{1}{\sqrt[]{3x}}-\frac{1}{\sqrt[]{15}}}{x-5}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

$$f\left(x\right)=\frac{1}{\sqrt[]{3x}}$$ Instantaneous rate at: $$x=5$$

$$f\left(x\right)=\frac{2}{\sqrt[]{1x}}$$ Instantaneous rate at: $$x=2$$

$$f\left(x\right)=\frac{4}{\sqrt[]{2x}}$$ Instantaneous rate at: $$x=3$$

$$f\left(x\right)=\frac{6}{\sqrt[]{3x}}$$ Instantaneous rate at: $$x=4$$

$$\lim_{h\rightarrow0}\ \frac{e^{6\left(3+h\right)+1}-e^{10}}{h}$$ The limit represents the instantaneous rate of change of a function. Identify the original function, and the x-value of the instantaneous rate of change.

$$f\left(x\right)=e^{6x+1}$$ Instantaneous rate at: $$x=3$$

$$f\left(x\right)=e^{4x+2}$$ Instantaneous rate at: $$x=5$$

$$f\left(x\right)=4^{3x+2}$$ Instantaneous rate at: $$x=2$$

$$f\left(x\right)=8^{2x+4}$$ Instantaneous rate at: $$x=6$$

Calculus Unit 2

Authored by Curtis Raynor

Mathematics

11th Grade

CCSS covered

Used 6+ times

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