Question

MATH 170-MAKE UP 1. Find the sum of the series $\sum_{n=0}^{\infty} (-1)^n \frac{\pi^{2n}}{6^{2n}(2n)!}$ 2. Find a formula for the distance D from the point $P_1(x_1, y_1, z_1)$ to the plane $ax + by + cz + d = 0$. 3. Find the length of the curve $\vec{r}(t) = <\cos t, \sin t, \ln \cos t>$, $0 \le t \le \pi/4$. 4. Find the curvature of $y = x^4$ at the point $(1,1)$.

          MATH 170-MAKE UP
1. Find the sum of the series
$\sum_{n=0}^{\infty} (-1)^n \frac{\pi^{2n}}{6^{2n}(2n)!}$
2. Find a formula for the distance D from the point $P_1(x_1, y_1, z_1)$ to the
plane $ax + by + cz + d = 0$.
3. Find the length of the curve
$\vec{r}(t) = <\cos t, \sin t, \ln \cos t>$,
$0 \le t \le \pi/4$.
4. Find the curvature of $y = x^4$ at the point $(1,1)$.

MATH 170-MAKE UP
1. Find the sum of the series
∑n=0^∞ (-1)^n (π^2n)/(6^2n(2n)!)
2. Find a formula for the distance D from the point P1(x1, y1, z1) to the
plane ax + by + cz + d = 0.
3. Find the length of the curve
r⃗(t) = <cos t, sin t, lncos t>,
0 ≤ t ≤π/4.
4. Find the curvature of y = x^4 at the point (1,1).

Added by Amy A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

12/05/2022

Step 1

To find the sum of the series, we need to determine the pattern of the terms. Looking at the series, we can see that the numerator is 2r and the denominator is 62n(2n)!. Show more…

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Texts: MATH 170-MAKE UP 1. Find the sum of the series ∑(2r) / (62n(2n)!) 2. Find a formula for the distance D from the point P(i,1,1) to the plane ax + by + c + d = 0. 3. Find the length of the curve ∫√(cos^2(t) + sin^2(t) + (In(cos(t)))^2) dt, 0 < t < π/4. 4. Find the curvature of y = 4 at the point (1,1).