| Topic | Problem | Solution |
|---|---|---|
| None | Evaluate the limit along the stated paths, or typ… | First, we substitute $x=0$ into the equation, we get $\lim _{y \rightarrow 0} \frac{y^{3}}{y^{2}}=\… |
| None | Use the elimination method to find all solutions … | Given the system of equations: \[\left\{\begin{array}{l} 3 x^{2}-y^{2}=11 \\ x^{2}+4 y^{2}=8 \end{a… |
| None | A man flies a small airplane from Fargo to Bismar… | Let's denote the speed of the plane in still air as 'p' (in mph) and the speed of the wind as 'w' (… |
| None | Suppose $\int_{-2}^{3} f(x) d x=45$ Then the aver… | Suppose \(\int_{-2}^{3} f(x) d x=45\) |
| None | A particle starts out from the origin. Its veloci… | A particle starts out from the origin. Its velocity, in miles per hour, after t hours is given by \… |
| None | Waldo sells $x$ pieces of fencing, and each bring… | Waldo sells \(x\) pieces of fencing, and each brings in revenue of \(r=30-2 x\) dollars. The fixed … |
| None | Suppose $f(x)$ has critical points at $x=2, x=1$,… | Given that $f(x)$ has critical points at $x=2, x=1$, and $x=-1$ and that $f^{\prime \prime}(x)=\fra… |
| None | Suppose $\int f(x) d x=\frac{16}{x}+12 \cdot 2^{-… | Suppose the integral of function f(x) is given by \(\int f(x) d x=\frac{16}{x}+12 \cdot 2^{-x}+16 \… |
| None | If $f^{\prime \prime}(x)=\frac{8}{x^{3}}$ and $f^… | Given that $f''(x) = \frac{8}{x^3}$, we can find $f'(x)$ by integrating $f''(x)$ with respect to $x… |
| None | Suppose we are told that $f(x)$ is a mystery func… | Given that $f(x)$ is a mystery function where $f((-50))=\ln (7)$ and $\lim _{x \rightarrow \infty} … |
| None | 4. Rewrite each of the following as an iterated d… | Define the region of integration for each integral by the given inequalities. |
| None | Prove $3^{2 n}-1$ is divisible by 8 . | We are given the problem to prove that \(3^{2 n}-1\) is divisible by 8 for any positive integer n. … |
| None | Use inductive reasoning to predict the next line … | Observe the pattern in the given sequence of computations. The left side of each equation is the su… |
| None | $D(x)$ is the price, in dollars per unit, that co… | Set the demand function equal to the supply function to find the equilibrium quantity: \(1500 - 10x… |
| None | The principal $P$ is borrowed and the loan's futu… | We are given the principal amount (P) as $2000.00, the future value of the loan (A) as $2720.00, an… |
| None | Until recently, hamburgers at the city sports are… | We are given two points on the demand curve: (3.4, 4000) and (4, 2500). We can use these points to … |
| None | The principal $P$ is borrowed at a simple interes… | We are given the principal $P = \$7000$, the interest rate $r = 1.5\% = 0.015$ (as a decimal), and … |
| None | Change the percent to a decimal equivalent. \[ 5 … | Change the percent to a decimal equivalent. We have \(5 \frac{9}{10} \%\). |
| None | Let two cards be dealt successively, without repl… | There are 4 sevens in a deck of 52 cards. So the probability that the first card drawn is a seven i… |
| None | Let two cards be dealt successively, without repl… | Let two cards be dealt successively, without replacement, from a standard 52-card deck. We are aske… |
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