Tema
Q:
(e) For what values of \( x \) is \( d \) smallest?
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. \( x= \)
(Type an integer or decimal rounded to two decimal places as needed. Use a comma to separate
answers as needed.)
B. \( d(x) \) gets infinitely small.
Q:
\( \int_{A B} z^{2} d z \), over the straight line going the points
\( A(1 ; 1) \) and \( B(2 ; 1) \)
Q:
Evaluate the integral
\[ \int \frac{d x}{(2 x+2)^{4}}, \]
by making the appropriate substitution: \( u=\square \)
Q:
Evaluate the integral
\[ \int x^{5}\left(x^{6}-8\right)^{21} d x, \]
by making the appropriate substitution: \( u=\square \)
Q:
Consider the indefinite integral \( \int \frac{x^{4}}{\left(x^{5}+3\right)^{5}} d x \) :
This can be transformed into a basic integral by letting
\( u=\square \) and
\( d u=\square \)
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
Consider the indefinite integral \( \int x \cdot \sqrt[2]{x^{2}+6} d x \) :
This can be transformed into a basic integral by letting
\( u=\square \) and
\( d u=\square \)
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
Evaluate the integral
by making the appropriate substitution: \( u=\square \frac{d x}{(2 x+2)^{4}} \),
\( \int \frac{d x}{(2 x+2)^{4}}=\square \)
Q:
Evaluate the indefinite integral.
\( \int \frac{5}{(t+3)^{2}} d t \)
\( \square+C \)
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