11 Evaluate the iterated integral. JJ, J, (x² + y² + z?) dx dy dz A 5 в) з D 10 00

Q: Question 10 Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B)…

A:

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

A:

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

A:

Q: |r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) = to find k(t). r(t) = 7 cos(4t)i+7 sin(4t)j + 5tk

A: Given problem:-

Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: E. Find the point of intersection of the plane 2x+3y+z 5 and the line x- 3 y+4 z- 1 1 II

A:

Q: Two particles travel along the space curves r(t)and u(t). (If an answer does not exist, enter DNE.…

A:

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

Q: Find V × (V × F) if F(x, y, z) = 4xyj+2xyz k. V × (V × F) :

A:

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

A:

Q: The graph of the first derivative f' of a function f is shown. (Assume the function is defined only…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 2 1 Evaluate the iterated integral. J J. J. (x² + y2 + z?) dx dy dz -1°0 A) 5 B 3 8 D) 10

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 5…

A:

Q: If the length of arc of a circle of radius 2/3 feet is 14 feet. then the central angle 0 is:

A: Given Radius of circle (r)=23feet & Length of arc (s)=14 feet To find central angle θ:

Q: 7-18 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7.…

A:

Q: 5 Sine cose do 1. Sine+ 3sine - 4

A: Indefinite integral

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 5 sin(t)j…

A:

Q: Find curl (3z i + 4x j + 6y k). curl (3z i + 4x j + 6y k) = ( i )i + ( i )j + ( i )k

A:

Q: (b) trte) × u(t)] dt (i) Find the product first, then differentiate. (ii) Apply the properties of…

A:

Q: (4x - lim (4x – V16x2 + 3x – 5

A: Topic:- limit calculation

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y3, P(4,…

A:

Q: The graphs of the function f (r) = 7- a and g(a) = 3 are given below. %3D 10 8 f(x) = 7-x2 4- g(x) =…

A: topic- area bounded by curves

Q: Find div F and curl F if F(x, y, z) = 13y"z'i – 10x°z*j – 7xy°k. div F= curl F=

A:

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

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

Q: |r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = ei + etj 30 е4 K(t) : e-t (25 el2t + 1)

A:

Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

A:

Q: d²s = 60/E – 18 subject to the conditions that ds = 5 and s= 11 when t= 1. Find the velocity v = dt…

A:

Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: f' (x) = 3x* – 5x² + x

A:

Q: dx 2.

A:

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: y=2\4-x²

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: 7. -4 3. ) dx - 3 10.

A: The given integral,         ∫e5xe2x7+3e3xdx

Q: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

A:

Q: Find the J(2x + 1)³ dx

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. ex f(x) [0, 6] 1 +…

A: maxima minima

Q: -4 = ニ 200

A: To solve for x using the the given equation.

Q: ах 2xy 2.xy +3y x +2xy dy dx

A:

Q: 3. Use an appropriate method of your choice to determine whether the given series converges. Clearly…

A:

Q: x'y'y'+ xy' = 1 dy x' + y' dx 2ху dy 2 rv + 3v2

A:

Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

A: Given: y=2x-6x=0 and x=4

Q: V4-x² c 3-x²-y² x dz dy dx J_5+x²+y² A 128/15 B 16/89 23/6 D) 6

A:

Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

Q: Find the volume of the solid generated by revolving the region R bounded by the graphs of the given…

A:

Q: Question8: Choose one answer. You decide to collect a bunch of cans of soda and measure the volume…

A: To solve the following problem

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) =…

A: The given function is: f(x)=e-5x

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

A:

Q: Find the following for the given equation. r(t) = ( + 6t)i + (t² – 6t)j %3D (a) r'(t) = (b) r"(t) =…

A: