ALL Problems

Topic	Problem	Solution
None	Find $(f + g) (x)$ when $f (x) = 5 x^{2} - 3 x + 1$ and $g(…	Given functions are $f (x) = 5 x^{2} - 3 x + 1$ and $g (x) = 2 x - 6$
None	a. For the function and point below, find $f^{\pr…	Given the function $f (x) = \frac{3}{\sqrt{x}}$ and the point $a = \frac{1}{4}$ .
None	Determine the following indefinite integral. Chec…	We are given the integral $\int \sqrt[5]{r^{4}} d r$ , which is of the form $\int x^{n} d x$ , where …
None	Suppose that the functions $g$ and $h$ are define…	We are given two functions, $g (x) = \frac{2}{x}$ and $h (x) = x^{2} - 4$ . We are asked to find the…
None	Part 1 of 5 Estimate the area under $f (x) = 3 x + 10$ …	We are asked to estimate the area under the curve $f (x) = 3 x + 10$ on the interval $[0, 3]$ using \(…
None	Use implicit differentiation to find $y^{'}$ …	The given equation is $x^{2} y - 3 x^{3} + 8 = 0$ . We need to find the derivative of $y$ with respect…
None	The graph of $f$ is translated a whole number of …	The graph of function f is translated a whole number of units horizontally and vertically to obtain…
None	10. Write the following in decimal notation: $9.5…	The question is asking to convert a number in scientific notation to decimal notation. In scientifi…
None	What is $f_{x}$ if $f (x, y) = x^{2} y^{2} + x^{y}$ ? …	The question is asking for the partial derivative of the function $f (x, y) = x^{2} y^{2} + x^{y}$ wit…
None	The cost of a scarf is twice that of a hat. 1 sca…	Let $x$ be the cost of a hat and $2 x$ be the cost of a scarf. We can then rewrite the problem a…
None	Three computers are chosen at random from an inve…	We are choosing 3 computers from an inventory of Dell and Acer computers. We are assuming that the …
None	The motion of a point on the circumference of a r…	Given the position vector function of a point on the circumference of a rolling wheel of radius 5 f…
None	At how many points does the graph of the function…	Given the quadratic function $y = 25 x^{2} - 10 x + 1$ , we are asked to find at how many points the graph…
None	Sebastian deposits $$ 1, 300$ every quarter into …	Given that Sebastian deposits $1300 every quarter into an account earning an annual interest rate o…
None	The logistic growth function $f(t)=\frac{105,000}…	The logistic growth function $f (t) = \frac{105, 000}{1 + 4600 e^{- t}}$ describes the number of people,…
None	A piece of rectangular sheet metal is 20 inches w…	The restrictions on $x$ are $0 < x < 10$ .
None	Find $\vec{T}, \vec{N}$ and $\vec{B}$ for the cur…	Given the curve $\vec{r} (t) = ⟨ 3 \cos (4 t), 3 \sin (4 t), 2 t ⟩$
None	Find the curvature of the curve $\vec{r}(t)=\lang…	Given the curve $\vec{r} (t) = ⟨ 4 \cos (3 t), 4 \sin (3 t), 4 t ⟩$
None	$x^{2} - 10 x + 25 = 0$	Given the quadratic equation: $x^{2} - 10 x + 25 = 0$
None	Find the difference. \[ \frac{8}{x^{2}-9 x}-\frac…	The problem is asking for the difference between two fractions. To find the difference between two …

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