| Topic | Problem | Solution |
|---|---|---|
| None | If we apply Rolle's Theorem to the function $f(x)… | First, we need to check if the function satisfies the conditions of Rolle's Theorem. The function \… |
| None | Consider the function $f(x)=2 x^{3}-5 x$ on the i… | Consider the function \(f(x)=2 x^{3}-5 x\) on the interval \([-3,3]\). We are asked to find the ave… |
| None | Given the function $g(x)=4 x^{3}+6 x^{2}-24 x$, f… | The derivative of a function can be found by applying the power rule, which states that the derivat… |
| None | Consider the function $f(x)=4 x+4 x^{-1}$. For th… | Given the function \(f(x)=4x+\frac{4}{x}\), we need to find the critical numbers and the value of x… |
| None | (1) $\mathrm{i}^{4 \mathrm{n}+3}$ (2) $i^{8 n+85}… | The problem is asking for the value of \(i^{4n+3}\), where \(i\) is the imaginary unit and \(n\) is… |
| None | Let $y=\tan (5 x+2)$. Find the differential $d y$… | Given the function \(y = \tan(5x + 2)\), we need to find the differential \(dy\) when \(x=5\) and \… |
| None | Find the area of the shaded region. \[ f(x)=10 x+… | The area of the shaded region between two functions, f(x) and g(x), from a to b is given by the int… |
| None | Find the area under the graph of $f$ over the int… | The function is a piecewise function, so we need to split the integral into two parts: one for the … |
| None | Find the center and the radius of the circle. The… | The given equation is already in the standard form of a circle equation, which is \(x^{2}+y^{2}=r^{… |
| None | Find the maximum and minimum values of the functi… | Define the function \(g(\theta)=2 \theta-9 \sin (\theta)\). |
| None | The function $f(x)=3+2 x+18 x^{-1}$ has one local… | Given the function \(f(x) = 3 + 2x + \frac{18}{x}\) |
| None | Use table for trigonometric function values of so… | From the angle addition formula, we have |
| None | Consider the function $f(x)=2-6 x^{2}, \quad-4 \l… | Consider the function \(f(x)=2-6 x^{2}\), for \(-4 \leq x \leq 2\). |
| None | Find the height of a pine tree that casts a 86 -f… | First, we need to convert the angle of elevation from degrees and minutes to decimal form. We know … |
| None | The function $f(x)=2 x^{3}-36 x^{2}+210 x-10$ has… | The function given is \(f(x)=2 x^{3}-36 x^{2}+210 x-10\). |
| None | $12-(-12)=$ | The question is asking for the result of subtracting negative twelve from twelve. In mathematics, s… |
| None | $\int \sin ^{2} x d x$ | Given the integral of \(\sin^2 x\) |
| None | Find the first and second derivatives. \[ y=\frac… | We are given the function \(y = \frac{2x^5 + 6}{x^3}\). |
| None | Required information An object moving at constant… | Let the original speed be $v$ and the original radius be $r$. The original acceleration is $a = \fr… |
| None | Suppose you're offered the following three accoun… | For the simple interest rate, the interest would be $10000 \cdot 0.15=1500$ dollars every year. Sin… |
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