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- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
Well, the image equation is a different equation? One has $\frac1 {2024}$ on the right, and the other has $2024$ on the right?
- Evaluating $\int_ {0}^ {1} \int_ {0}^ {1} \int_ {0}^ {1} \sqrt { {x^2+y . . .
I would like to know how to evaluate the following triple integral with the help of spherical coordinates $$\int_ {0}^ {1} \int_ {0}^ {1} \int_ {0}^ {1} \sqrt { {x^2+y^2+z^2}} \,dx \,dy\, dz$$ The relations
- calculus - Evaluating $\int {\frac {x^ {14}+x^ {11}+x^5} { (x^6+x^3+1 . . .
The following question is taken from JEE practice set Evaluate $\displaystyle\int {\frac {x^ {14}+x^ {11}+x^5} {\left (x^6+x^3+1\right)^3}} \, \mathrm dx$ My
- Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1 2x}}{x} $ without . . .
The following is a question from the Joint Entrance Examination (Main) from the 09 April 2024 evening shift: $$ \lim_ {x \to 0} \frac {e - (1 + 2x)^ {1 2x}} {x} $$ is equal to: (A) $0$ (B) $\frac {-2} {
- integration - Evaluating $\iiint z (x^2+y^2+z^2)^ {−3 2}\,dx\,dy\,dz . . .
Spherical Coordinate Homework Question Evaluate the triple integral of $f (x,y,z)=z (x^2+y^2+z^2)^ {−3 2}$ over the part of the ball $x^2+y^2+z^2\le 81$ defined by
- Evaluating $\\prod_{n=1}^{\\infty}\\left(1+\\frac{1}{2^n}\\right)$
Compute:$$\prod_ {n=1}^ {\infty}\left (1+\frac {1} {2^n}\right)$$ I and my friend came across this product Is the product till infinity equal to $1$? If no, what is the answer?
- Evaluating $\\int_0^{\\infty}\\frac{\\ln(x^2+1)}{x^2+1}dx$
How would I go about evaluating this integral? $$\int_0^ {\infty}\frac {\ln (x^2+1)} {x^2+1}dx $$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the complex p
- Evaluating $\lim_ {x\to 1}\frac {\left (\sum_ {k=1}^ {100}x^k\right . . .
$$\lim_ {x\to 1}\frac {\left (\sum_ {k=1}^ {100}x^k\right)-100} {x-1}$$ So I tried to do this problem with 2 methods Method 1 gives me the correct answer whereas method 2 doesn't Can someone help me po
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