Tema
Q:
Evaluate the definite integral.
\( \int_{0}^{3}(x-3)^{2} d x \)
Q:
Find the general solution for the differential equation.
\( \frac{\mathrm{dy}}{\mathrm{dx}}=8 e^{3 \mathrm{x}} \)
Q:
Find the cost function if the marginal cost function is \( C^{\prime}(x)=18 x-11 \) and the fixed cost is \( \$ 6 \).
A. \( C(x)=9 x^{2}-11 x+6 \)
B. \( C(x)=18 x^{2}-11 x+6 \)
C. \( C(x)=9 x^{2}-11 x+5 \)
D. \( C(x)=18 x^{2}-11 x+5 \)
Q:
Find \( C(x) \) if \( C^{\prime}(x)=\sqrt{x} \) and \( C(9)=40 \)
A. \( C(x)=\frac{2}{3} x^{3 / 2}+31 \)
B. \( C(x)=2 x^{3 / 2}+31 \)
C. \( C(x)=2 x^{3 / 2}+22 \)
D. \( C(x)=\frac{2}{3} x^{3 / 2}+22 \)
Q:
1.3 The parametric equations for an ellipse are \( x=4 \cos (\theta), y=\sin (\theta) \)
Find \( \frac{d y}{d x} \)
Q:
Find the integral.
\( \int\left(5 x^{2}+1\right) d x \)
Q:
1.3 The parametric equations for an ellipse are \( x=4 \cos (\theta), y=\sin (\theta) \)
Find \( \frac{d y}{d x} \)
Q:
A population of bacteria grows at a rate of \( \mathrm{P}^{\prime}(t)=30 e^{\mathrm{t}} \), where \( t \) is time in hours. Determine how
much the population increases from \( \mathrm{t}=0 \) to \( t=3 \). Round your answer to two decimal places.
A. 572.57
B. 602.57
C. \( 1,175.14 \)
D. 587.57
Q:
Question
Find the most general antiderivative (including the constant term, \( C), F(x) \) given the function below.
\[ f(x)=\tan (x)(4 \cos (x)+8 \sec (x)) \]
Provide your answer below:
\( F(x)=\square \)
Q:
\( \int _{}^{}(\frac{5}{\sin (x^{2})-3x^{2}+e^{x}}) d x \)
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