Skatch the curve in polar coordinates. r=I+ 3sino 2 -6 -4 -4

Q: Find the interval and the radius of convergence for the series n=1 n2"

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Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: P(x) Let P(x) and Q (x) be polynomials with the degree of Q (x) greater than the degree of P (x) and…

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Q: tan(0)² cos(0) d0

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Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

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Q: Find r(t) for the given conditions. r"(t) = -4 cos(t)j – 3 sin(t)k, r'(0) = 3k, r(0) = 4j %3D %3D…

A: Given

Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

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Q: ||r(t) × r"(t)|| ||r'(t)||* Use the formula k(t) : to find k(t). r(t) = e"i+ ej K(t) :

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Q: f(x, y) = x3 - y³, P(4, 3), v = (i+ j) %3D 2

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y= 0, y = 7+a*…

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Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

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Q: Show

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Q: Solve the following differential equations of 1- yy' = 2y – x; r'y'y'+ xy' = 1 dy x + v

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Q: 8. The ideal gas law PV volume, and temperature of a confined gas, where n is the number of moles of…

A: We need to prove the statement.

Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: E(-1)n+1_2 Vn n=1

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Q: Find div F and curl F if F(x, y, z) = 6e#Y i – 7 cos yj+ 9 sin² z k. div F= curl F=

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

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Q: 27х3-8а3 y3= y= 3x-2a Зх-2а

A: Y'=?

Q: If f is continuous at a number, x, then f is differentiable at x. True False

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Q: Given h(r) = 1/r+3 find the following: (a)h(x2)= (b) h(x2 + 1)= (c)h(x2) + 1=

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Q: Find div F and curl F if F(x, Y, z) = x°i – 4j + yzk. div F= curl F=

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Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

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Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: the

A: We will find the derivative.

Q: Find the area between the curve y=2 and the chord joining the points (0,1) and (2,4). O 0.5608 O…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Find the principal unit normal vectóř tô thể curve at the r(t) = /2ti + e'j + e-k, t = 0 %3D

A: Principal unit normal vector

Q: 2" 5n+1 n=1

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Solution: ∯∂∂x6xy -∂∂y3xydxdy   (By green's theorem)

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 24x from (24, 24) to (0,0). NOTE:…

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Q: A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or…

A: Here, the region is bounded by the curves: x=4, y2=x

Q: (9, -7) (3, 1). Find 吕 ロ师仁 ?

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Q: 6 + (-3) + 0 + ..+ 411 = 97 (a* + 5) - 0 k = 1

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: (1 point) Use the Divergence Theorem to calculate the flux of the vector fields F, = -Szi + 5xk and…

A: Find your answer below

Q: Find the general solution: y" + 4y' + 6y = 0.

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Q: 1. Sketch a single graph of a function f(x) which satisfies all of the following the limits and…

A: The function satisfies,f-3=1, limx→-4f(x)=-1, limx→2-f(x)=-∞, limx→2+f(x)=∞, f'(4)=0f(2)=2,…

Q: 1. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of…

A: The solution is given in the next steps.

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) : = 6ti –…

A: Solution is done in step 2

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: mparison test to determine whether the given series conve:

A: Please refer to the image below

Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

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Q: Find div F and curl F if F(x, y, z) = x'i – 3j + yzk. div F= curl F=

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Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

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Q: Given that f'(x) is continuous everywhere and changes from negative to positive at x=a, which of the…

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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