009A Sample Final 2, Problem 8

Compute

(a) $\lim _{x\rightarrow \infty }{\frac {x^{-1}+x}{1+{\sqrt {1+x}}}}$

(b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\rightarrow 0} \frac{\sin x}{\cos x-1}}

(c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\rightarrow 1} \frac{x^3-1}{x^{10}-1}}

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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