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Finding the range and domain of $f(x)=\tan (x)$
I am attempting to find the range and domain of $f(x)=\tan(x)$ and show why this is the case. I can seem to find the domain relatively well, however I run...
Apr 16, 2026
Archive: News
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How do I find the Maclaurin series of $\sinh^2(x)$?
Essentially what the title says. I'm asked to find the Taylor polynomial of degree $n$ for $f(x)=\sinh^2(x)$ about $a=0$. This is essentially a Macla...
Apr 16, 2026
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What does f(•) mean?
I'm reading the calculus test's answers and the professor wrote that representing the function. I wonder what the dot inside means. "Given a fun...
Apr 16, 2026
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Impulse response of integrator
I want to get the impulse response of an LTI system where $$y(t) = \int_{t-2T}^{t-T} x(\alpha) d\alpha $$ To solve this I did: $$h(t) = \int_{t-2T}^{t-T} ...
Apr 16, 2026
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Differential Equations, unique solution
Just had a quick question regarding the uniqueness of the general solution of first-order differential equations: For $x'(t)=Ax(t)$ where $A$ is an $...
Apr 16, 2026
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Finding an equation of a quadratic function given 2 points?
I'm doing a maths problem in which a part of roller coaster track is missing. The gap must be filled by a polynomial equation and we know that it mus...
Apr 16, 2026
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Finding volume by rotation of a triangle
The following problem is from the book, Calculus and Analytical Geometer by Thomas and Finney. Problem: Find the volume generated by revolving the followi...
Apr 15, 2026
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Relative maximum and minimum of function of three variables
I know that how to find relative maximum and minimum of function of two variables. How can I determine function when $f(x,y,z)=x^2+y^2-z^2 $ has relative ...
Apr 15, 2026
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Limit of a fraction at infinity when all terms go to zero
Suppose $Y = \sum_{j = 1}^{(n-1)!} \prod_{i = 1}^{n-1} y_{ij}$ and $Z = \sum_{j = 1}^{(n-1)!} \prod_{i = 1}^{n-1} z_{ij}$. Also suppose $0 < x < 1$,...
Apr 15, 2026
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If $\log_8 3 = P$ and $\log_3 5 = Q$, express $\log_{10} 5$ in terms of $P$ and $Q$.
If $\log_8 3 = P$ and $\log_3 5 = Q$, express $\log_{10} 5$ in terms of $P$ and $Q$. Your answer should no longer include any logarithms. I noted that $\l...
Apr 15, 2026
