Find curl (4z i+ 5x j+ 8y k). curl(4z i+ 5x j+ 8y k) = ( )i +( i j+( i )k

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: Find the sum of the convergent series. 4 Σ n(n + 2) n = 1

A:

Q: Consider the change of variable u = xy and v = 3y + 2x and the integral 2.r + 3y – 6 =0 - ||. (2r²y…

A:

Q: x2 + x – 2 At which value of x does the function f(x) have a removable discontinuity? g3 – 3x2 + 2x

A:

Q: 2 Integrate | 20(5æ – 3)°dæ - – 2

A:

Q: 2.x4 + x3 x4 xp-

A: Given query is to find the value of the integral.

Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x, x = 2, x = 5 and y =…

A:

Q: Let L be the line r(t)=(1+1,1-2r,3+5t) and II be the plane 2x-y+3z-48=0. a Find the point of…

A:

Q: In t years, the population of a certain city grows from 700,000 to a size P given by P(t)= 700,000 +…

A:

Q: uppose the area of the region betwe =b is 3 square units. Find the area be

A:

Q: A particle is moving with acceleration a(t) = 18t + 4. its position at timet = 0 is s(0) = 6 and its…

A: Solution of given question is written in below steps.

Q: Solve the following differential equations of dy 1 y= xy': + dx

A:

Q: •5 f(x)dx = 6 and | g(x)dx= 2 , evaluate |3|

A:

Q: 4. Evaluate lim (cos r)/". エ→0

A: we want to find the limit limx→0 ( cosx )1x2

Q: Find the area oF the regioN eNclosed between the curves de Fived by the equations y =Vx +2, y: x,…

A:

Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

Q: 1. A bumblebee was released and started to travel along a straight horizontal line. The directed…

A:

Q: The surface S i parametrized by equations x = u + v, y = 3u², z = u – v; The point P (2, 3, 0) lies…

A: Given that the surface S is parameterized by equations x=u+v, y=3u2,z=u-v; the point P(2,3,0) lies…

Q: It can be shown that the polar curve r = a sin(0) +b cos(0), where ab + 0, is a circle. Find the…

A:

Q: [1 1 3 3 1 3 3 0 2 1 1 1 1 2 0 1 2 1 0 1 1 3 6 2 1 4 2 3 2 1 2 4 2 1

A:

Q: Solve the initial value problem using Laplace transforms. y" - y' – 6y = 2, y(0) = 0, y'(0) = 0

A: We need to solve the IVP given.

Q: 8. 1 +3 + 3² + . + 3"-1 = (3" - 1) (3"- 1) ...

A:

Q: Evaluate the integral. Show that the substitution x = V6 sec(0) transforms I into fcos(0) d0, and…

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: Solve for the gradient of the given function. f(x, y) = e¤ sin y + el cos x

A: Given,  f(x,y)=ex sin y+ey cos x

Q: Use the principle of mathematical induction to show that the given statement is true for all natural…

A: Question number 6 has been solved as per the requirement of the student.   This question can be…

Q: evaluate the region S

A: answer is in next step

Q: Given s(t)= 21+21, where s(t) is in feet and t is in seconds, find each of the following a) v(1) b)…

A:

Q: Let 7 (t) = < 5t? + 5, tª + 3t, In a. Determine the coordinates of the point on the curve traced out…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t= 2 6 0 , V37 1 T V37…

A: SEE EXPLANATION

Q: Evaluate the integral. dx (х — 9)(х — 18) (Use symbolic notation and fractions where needed. Use C…

A:

Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i+ 11 sin(t)j + tk; t= 2 T() - T N 2.

A:

Q: What is the area of the region bounded by the graph of r = 4 cos 20? Choose two (2) correct answers.…

A: Let's find.

Q: (c) Show that the differential equation ry" – 3y + zy = 0 has a general solution of the form y(z) =…

A: given that differential equation   xy'' - 3y' + xy = 0…

Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

A: In this question we have to find the minimum amount of tin sheet that can be made into a closed…

Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

A:

Q: Let 7(t) = Find )dt (don't include the +C)

A:

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (-2, -3) in the direction 0 =…

A:

Q: sincxt sintpx)dx -元 -IK 1/0

A: 1π∫-ππsinx sin(px) dxusing property∫-aaf(x) dx= 2∫0af(x) dx ;  f(-x)=f(x)=1π×2∫0πsinx sin(px)…

Q: Find V · (V × F), if F(x, y, z) = 2e"*i+4xe"j – 4c*k. V · (V × F) =

A:

Q: Using Euler's Method, approximate the initial value problem for various values of x given in the…

A:

Q: 2. Let f(x) = VI(2 – x)². Use the local linear approximation of f(x) at ro = 1 to estimate V0.99…

A: f(x)=x2-x2The linear approximation of f(x) at x0=1

Q: Ben is a fisherman with a boat in Rhyl harbour. This is part of a graph of the depth of water at the…

A:

Q: a) Graph the function f(x) = 2x -5x+3 b) Draw a tangent line to the graph at the point whose…

A: Given the function is  f(x) = 2x2-5x+3

Q: (y – x) dx + 15x?y? dy

A: answer is in next step

Q: Find the equation of the tangent to the graph of f(x) = x-3 at the point (5, 4). Start by evaluating…

A:

Q: 1 Answer: diverges n In n n=2

A:

Q: sinex) sintpx) x

A:

Q: Find the area between the loops of the limacon r = 7(1+ 2 cos 0). Area =

A:

Q: n2 series E(-1)"+1- converges or n3 +1 n=1

A: Given