Topic
Q:
(3) \( \lim _{x \rightarrow 3} \frac{x-3}{x^{2}-4 x+3} \)
Q:
8. \( \int \cos (b+a x) d x \)
Q:
Find the integral.
\( \int \frac{x}{\left(7 x^{2}+3\right)^{5}} d x \)
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(5) \( \lim _{x \rightarrow 0} \frac{\frac{1}{x+7}-\frac{1}{7}}{x} \)
Q:
(5) \( \lim _{x \rightarrow 0} \frac{\frac{1+1}{x+i}-\frac{1}{7}}{x}= \)
Q:
Question
We are trying to prove the following limit.
\[ \lim _{x \rightarrow-\infty}\left(\frac{4 x^{4}+7 x-1}{-6 x^{4}+9 x+5}\right)=-\frac{2}{3} \]
One of the steps in the proof is to show that for every \( \varepsilon>0 \) there is a corresponding negative number \( N \) such that
\[ \text { if } x<N, \text { then }|\square|<\varepsilon . \]
Fill in the blank (shown as a square box) for this statement.
Provide your answer below:
If \( x<N \), then \( |\square|<\varepsilon \).
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Question
Consider the function \( f(x) \) below. Over what interval(s) is the function concave up? Give your answer in interval notation
and using exact values.
\[ f(x)=7 x^{4}-4 x^{2}-8 x-5 \]
Provide your answer below:
Q:
Question
Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate.
\[ \begin{aligned} f(x)=2 x+2 \ln (x)-5 \\ g(x)=2 x+4\end{aligned} \]
\[ \]
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10. \( \lim _{x \rightarrow(\pi / 2)^{+}} \frac{\cos x}{1-\sin x} \)
Q:
Question
Using L'Hospital's rule, determine whether \( f(x) \) or \( g(x) \) given below grows at a faster rate.
\[ \begin{array}{l}f(x)=x^{3}+3 x^{2}+4 \\ g(x)=3 \ln (x)^{2}\end{array} \]
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