Chapter 2

Limits

Educators


Problem 1

$$\lim _{x \rightarrow 8}\left(x^{2}-5 x-11\right)=$$

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Problem 2

$$\lim _{x \rightarrow 5}\left(\frac{x+3}{x^{2}-15}\right)=$$

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Problem 3

$$\lim _{x \rightarrow 3}\left(\frac{x^{2}-2 x-3}{x-3}\right)=$$

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Problem 4

$$\lim _{x \rightarrow \infty}\left(\frac{x^{4}-8}{10 x^{2}+25 x+1}\right)=$$

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Problem 5

$$\lim _{x \rightarrow \infty}\left(\frac{x^{4}-8}{10 x^{4}+25 x+1}\right)=$$

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Problem 6

$$\lim _{x \rightarrow 6^{+}}\left(\frac{x+2}{x^{2}-4 x-12}\right)=$$

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Problem 7

$$\lim _{x \rightarrow 6^{-}}\left(\frac{x+2}{x^{2}-4 x-12}\right)=$$

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Problem 8

$$\lim _{x \rightarrow 6}\left(\frac{x+2}{x^{2}-4 x-12}\right)=$$

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Problem 9

$$\lim _{x \rightarrow 0^{+}}\left(\frac{x}{|x|}\right)=$$

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Problem 10

$$\lim _{x \rightarrow 7^{+}}\left(\frac{x}{x^{2}-49}\right)=$$

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Problem 11

$$\lim _{x \rightarrow 7}\left(\frac{x}{x^{2}-49}\right)=$$

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Problem 12

$$\text{ Let }f(x)=\left\{\begin{array}{l}{x^{2}-5, x \leq 3} \\ {x+2, x>3}\end{array}\right.$$
$$\text{Find} (a.)\lim _{x \rightarrow 3^{-}} f(x),(b) \lim _{x \rightarrow 3^{3}} f(x) \text { and }(\mathrm{c}) \lim _{x \rightarrow 3} f(x)$$

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Problem 13

$$\text{ Let } f(x)=\left\{\begin{array}{l}{x^{2}-5, x \leq 3} \\ {x+1, x>3}\end{array}\right.$$
$$\text{ Find } (a) \lim _{x \rightarrow 5^{-}} f(x),(b) \lim _{x \rightarrow 3^{+}} f(x) ; \text { and }(c) \lim _{x \rightarrow 3} f(x)$$

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Problem 14

$$\text{ Find }\lim _{x \rightarrow \frac{\pi}{4}} 3 \cos x$$

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Problem 15

$$\text{ Find }\lim _{x \rightarrow 0} 3 \frac{x}{\cos x}$$

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Problem 16

$$\text{ Find }\lim _{x \rightarrow 0} 3 \frac{x}{\sin x}$$

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Problem 17

$$\text{ Find }\lim _{x \rightarrow 0} \frac{\tan 7 x}{\sin 5 x}$$

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Problem 18

$$\text{ Find }\lim _{x \rightarrow \infty} \sin x$$

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Problem 19

$$\text{ Find }\lim _{x \rightarrow \infty} \sin \frac{1}{x}$$

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Problem 20

$$\text{ Find }\lim _{x \rightarrow 0} \frac{\sin ^{2} 7 x}{\sin ^{2} 11 x}$$

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Problem 21

$$\text{ Find }\lim _{h \rightarrow 0} \frac{(3+h)^{2}-9}{h}$$

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Problem 22

$$\text{ Find }\lim _{h \rightarrow 0} \frac{\frac{1}{x+h}-\frac{1}{x}}{h}$$

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