3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

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

A: Vector equation of a line passing through P(a,b,c), Q(p,q,r) is given by,…

Q: dx dy =

A:

Q: Evaluate the integral / (2x + 3y)dx + (6x – y)dy along the parabolic arc y = x' from (0,0) to (1,1).…

A:

Q: Find the area of the region enclosed by the curves y = x² and y 4.x by integrating with respect to…

A:

Q: Question 2 Use spherical coordinates to find the volume of the solid. The solid enclosed by the…

A:

Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5, x=4, and…

A:

Q: (c) Sketch a graph of the path, and sketch the velocity and acceleration vectors at the given point.…

A:

Q: Evaluate the definite integral. 9ti + 3t°j + Vtk) dt

A: The given definite integral,    ∫-119t i+3t3j+t3kdt

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

A: Solution:

Q: Question 7 Find the area of the region(s) enclosed by the curve f(x) = x³, the x-axis, and the lines…

A:

Q: Find the Laplace transform of: 1. f(t) = e(3t-7) cos³(6t) %3|

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: .

A:

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

A:

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

A:

Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) j+…

A:

Q: Consider the following functions. f(x) = 4 sin x g(x) = 4 cos 2x Sketch the region bounded by the…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 51…

A:

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

A:

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

A: To evaluate the length of the given curve.

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t+o 5t2 + 6't (?,?) - (

A: We have to find limit of given function

Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…

A: tangent property

Q: Find the approximate area under the curve of (X) = x²+1 from x = 0 to x = 2, using 4 left- endpoint…

A:

Q: Evaluate the line integral / (6x + 8y)dx + (4x – 8y)dy along the curve C: x = 2 cos t, y = 4 sint…

A:

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: lim 48V x 487Y

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

A:

Q: n? +1 2. Determine whether the series is convergent or divergent. If it's 2n² +1 n=1 convergent,…

A: The given series,        ∑n=1∞n2+12n2+1

Q: Question 2 Use double integration to find the volume of the solid bounded by the paraboloid z = 9x2…

A:

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

A:

Q: 2а-2х V4a-V4x

A:

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Let's find.

Q: Evaluate the triple integral. /I| ry sin(yz) dV, G where G is the rectangular box defined by the…

A:

Q: Find the approximate area under the curve of f (x) =cos (5) from x = 0 to x = TT, using 4…

A: Here, the interval [0,π] is divided into 4 intervals of the length of each interval is ∆x=π-04=π4.…

Q: Express the area of the given surface as an iterated double integral, and then find the surface…

A: We have to find the surface area.

Q: Evaluate the triple integral. zy sin(yz) dV , where G is the rectangular box defined by the…

A:

Q: Find V x (V × F) if F(x, y, z) = 6xyj+7xyzk. V × (V × F)

A:

Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A:

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A:

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Given the following functions: f(x) = cos(x) g(x) = x + 1 Find f(g(x)) and 8(S(x). (Use symbolic…

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: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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

A:

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

A:

Q: (b) Evaluate the velocity vector and acceleration vector of the object at the given point. %3D %3D…

A: As you mentioned part b is solved