| Topic | Problem | Solution |
|---|---|---|
| None | For $f(x)=\frac{4}{x+4}$ and $g(x)=\frac{3}{x}$, … | Given the functions $f(x)=\frac{4}{x+4}$ and $g(x)=\frac{3}{x}$, we are asked to find the compositi… |
| None | Question 2 (20 Points) Find the vertical and hori… | Find the vertical and horizontal asymptotes of the function \(y=\frac{1}{x+3}-2\) |
| None | Use l'Hôpital's rule to find the limit. \[ \lim _… | The given expression is \(\frac{2 x^{2}}{\cos x-1}\). However, this is not in the form of 0/0 or ∞/… |
| None | For the function $-x^{4}+x^{3}-6 x^{2}$ when $x \… | The function given is \(-x^{4}+x^{3}-6 x^{2}\). |
| None | Rewrite the ratio so that the units in the numera… | Rewrite the ratio so that the units in the numerator and the denominator are the same. Use values i… |
| None | Identify the coordinates of any local and absolut… | First, we need to find the derivative of the function \(y = 2\sqrt{3}x + 4\cos(x)\). The derivative… |
| None | a. Find the open interval(s) on which the functio… | First, we need to find the derivative of the function \(g(x) = x \sqrt{18 - x^2}\). |
| None | For the function $f(x)=\frac{x^{\frac{1}{3}}}{5}$… | \(f^{-1}(x)\) is defined as the number \(y\) such that \(f(y)=x\). Thus, we solve the equation \(\f… |
| None | Find parametric equations for the line tangent to… | The given surfaces are $x+y^{2}+2 z=5$ and $x=0$. The point of tangency is $(0,1,2)$. |
| None | Using the Method of Undetermined Coefficients, de… | The given differential equation is \(y^{\prime \prime}+81 y=6 t^{3} \sin 9 t\). |
| None | In 1859 , a person sold a house to a lady for $\$… | First, we calculate the number of years from 1859 to 2011, which is 152 years. |
| None | If $f(x)=5-9 x$, find $f^{-1}(2)$ Your answer is | The question is asking for the inverse of the function \(f(x) = 5 - 9x\) at the point 2. The invers… |
| None | The longest side of an acute triangle measures 30… | Given the longest side of an acute triangle measures 30 inches, and the two remaining sides are con… |
| None | Which best describes the diameter of a circle? A.… | The diameter of a circle is the distance across the circle through its center. |
| None | (a) Find the inverse function of $f(x)=7 x-6$. \[… | The inverse function of a function can be found by swapping the x and y values and solving for y. I… |
| None | Let \[ f(x)=\frac{1}{3} x-5, \quad 4 \leq x \leq … | Let \(f(x)=\frac{1}{3} x-5, \quad 4 \leq x \leq 9\) |
| None | Assume that the function $f$ is a one-to-one func… | Assume that the function $f$ is a one-to-one function. |
| None | Let $f(x)=\frac{1}{x-2}$ and $g(x)=\frac{2}{x}+2$… | Let \(f(x)=\frac{1}{x-2}\) and \(g(x)=\frac{2}{x}+2\). |
| None | Let $f(x)=2 x^{2}-7 x+5$ and $g(x)=x^{2}+16$. Fin… | First, we need to find the sum of the functions $f$ and $g$. This is done by adding the correspondi… |
| None | $\$ 17,818$ is invested, part at $11 \%$ and the … | Let's denote the amount invested at 11% as x and the amount invested at 6% as y. We know that the t… |
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