Topic
Q:
In Exercises \( 6-8 \), Evaluate the following. Show all the steps like we did in our class to
earn the credits.
6. \( \int_{1}^{4} \frac{-2 \log _{2} x}{x} d x \). NOT allowed to use Chegg or other such websites. NO Desmos, Calculator
and/or any other graphing website and/or utilities.
(a) Change the base
(b) Let \( \mathrm{z}=\ln \) ( )
(c) From part (b) find \( d z= \)
(d) Use parts (a) -(c) to write the definite integral in terms of z
(e) Integrate part(d) and write your final answer in simplest form.
Q:
\( y^{\prime \prime}=2 y^{\prime}+y=6 x e^{x} \)
\( \quad \) por coeficientes interminado
Q:
\( A = \int _ { \frac { 1 } { 2 } } ^ { 5 } \frac { 1 } { x } + 1 \)
Q:
Sigurentes limites:
\[ d \cdot \lim _{x \rightarrow 5} \frac{x-5}{x^{2}-25} \]
Q:
\( \int \cot ^ { 3 } x \cdot \csc ^ { 5 } x d x \)
Q:
Calcular \( \lim _{x \rightarrow 2} \frac{x^{2}-5 x+6}{x^{2}-3 x+2}= \)
Q:
\( ( 3 x + 6 y ^ { 2 } ) d x + 3 x y d y = 0 \)
Q:
\( \int \cot ^ { 3 } x \cdot \csc ^ { 5 } x d x \)
Q:
Question
Use the first derivative test to find the location of all local extrema in the interval \( (-5,0) \) for the function given below.
\[ f(x)=-3(x+2) e^{4 x} \]
If there is more than one local maximum or local minimum, write each value of \( x \) separated by a comma. If a local
maximum or local minimum does not occur on the interval, enter \( \varnothing \) in the appropriate box. Enter exact answers.
Q:
\( ( x y + y ^ { 2 } ) d x + ( x ^ { 2 } + 3 x y ) d y = 0 \)
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