(b) A spring exerts a force of 4.2N when stretched 0.7m beyond its natural length. How far beyond its natural length the spring can be stretched with 6.75J of work? Enter the exact answer.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

A:

Q: In this question, the power series method is to be applied to find the general solution of a…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y= x² between x…

A:

Q: Find the center of mass of the given system of point masses lying on the x-axis. m = 8, m, = 3, m, =…

A:

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

A:

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: What is the volume of the largest cone having its circular base circumscribed about a face of a…

A: To determine the volume of the largest cone having its circular base circumscribed about a face of a…

Q: 1. Set up the following improper integrals by definition. sin(x) dx 22 — За — 4 а. xe dx с. 4 et b.…

A:

Q: Find the directional derivative of the function at P in the direction of v f(x, y) = x³ - y³, P(6,…

A: we have to find directional derivative.

Q: Question 8 sine 1/2 I r cos e dr de. Evaluate the iterated integrals J. (A) 1/6 (в) 1/2 (D 11/9

A:

Q: True or False, and give a short reason: (a) If a function is differentiable, then it is continuous.…

A: Given problem:- True or False, and give a short reason:   (a) If a function is differentiable, then…

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x' and…

A: Solution:

Q: Find the exact arc length of the curve over the stated interval. 1 1 + from y = 1 to y = 3 x = NOTE:…

A: Aec length of the given curveL=∫131+dxdy2dy    Considerx=16y3+12y-1thendxdy=(16×3y2)+-12y2…

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

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: Edit Find div F and curl F if F(x, y, z) = 13y*z'i – 11x°2°j – 5xy'k. div F= 0 curl F= k (-55 a' 2º…

A:

Q: Question 11 /4-x² c 3-x²-y² STS xdz dy dx Evaluate the iterated integral. J. J. -5+x²+y? 0, A)…

A:

Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A:

Q: al)= gi+ sk vio)= 5), ro) 0

A:

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

A:

Q: Question 18 Find the surface area of that portion of the surface 2 = V4 -x that lies above the…

A:

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A:

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given

Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

A:

Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

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

A: The given integral,         ∫e5xe2x7+3e3xdx

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

A:

Q: given point. Function Point f(x, y, z) = V x2 + y2 + z² (10, 3, 9) %3D Vf(10, 3, 9) = Find the…

A:

Q: Find the length of the curve, L. y? = 64 (x + 5)* , 0 0

A: The solution is given in the next step.

Q: Find V· (V × F), if F(x, y, z) = 7e2*i+9xe³j – e=k. V · (V × F)

A:

Q: Find the centroid of the region. NOTE: Enter the exact answers. (¤, g) = |(?, ?) %3D y = =? 1

A: y=x7

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

A:

Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere x² + y?…

A:

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 7 cos(t)i…

A:

Q: Find the area of the region(s) enclosed by the curve (x) the x-axis, and the lines x = -1 and X= 2.…

A:

Q: Use a double integral to find the volume under the plane z=38x+y and over the rectangle…

A: We have to find the volume using double integration.

Q: Find the approximate area under the curve of f (X) =cos ( from x =0 tox=T, Using 4 trapezoids. 3 2.6…

A:

Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given

Q: Express the iterated integral as an equivalent integral with the order of integration reversed.…

A: Express the iterated integral as an equivalent integral with the order of integration reversed.

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

A:

Q: Where is each function continuous? (a) f(x) = Vi %3D

A: According to the company rule we can answer only first question and rest can be reposted.

Q: ... 3x+ 2y + 4z = 12 12 15

A:

Q: Find the area of the region bounded by the graphs of f (x) = x° and g (x) = x. (А) 1 B c) 0.5 D 3

A: