Find V · (V × F), if F(x, y, z) = 5e²i+ 5xe®j– 7ev²k. %3D V ·(V × F) =

Q: Find the exact area under the curve between the indicated values of x. 3 ; between x = 1 and x = 3

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: dy = xe with y(0) = 4 dx

A:

Q: The number N of beavers in a given area after x years can be approximated by the following. N = 5.5…

A: Given  population of beavers in a given area after x area N=5.5×100.23x    ,  0≤x≤10

Q: 3/2 dy The order and degree of the differential equation (). - 4 = 0 dx - dx2

A:

Q: Total cost from marginal cost. Shelly's Roadside Fruit has found that the marginal cost of producing…

A:

Q: Ow dw Find dx' dy and dz using implicit differentiation. Leave your answers in terms of x, y, z, and…

A:

Q: F (x) = f (t³ – t)°dt. Find the derivative of O 5(t – t)* (3t² –- 1) (23 – z)* O 5(2³ – z)“ O 3t2 –…

A: To FInd:  derivative of the given function

Q: Exercises Distinct Real Roots of Auxiliary Equation Find the general solution 5. (D² – 1)y = 0

A:

Q: Each of the following statements is an attempt to show that a given series is convergent or…

A:

Q: Product/Quotient/Chain Rules for Differentiation: Answer the following

A: Differentiation

Q: d 5x+3 4. dx 7x+2

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 And c·f'=c·f' ; where…

Q: Find the area of the region bounded by y = (1/8)(-x² + 6x + 7) and y = -6. Answer: Find the area of…

A:

Q: Solve the De as follows via Laplace transformations: y"- (14/3)y" - (55/3)y' + 14y = 0; y(0) = -1,…

A:

Q: The linear system with corresponding augmented matrix 2 -1|4 is consistent. True False « Previous…

A:

Q: Find the area bounded by the indicated curves. y = (x - 1)2, y = 8x - 24, where 3 s x s 5 Optional…

A: Let us draw the graph.

Q: Express the derivative in "subscript" notation. NOTE: Your answer should take the form fo. dy dx?

A: Consider  ∂3y∂y∂x2=

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A:

Q: dy + 2ху dx %3D

A: integrating factor method.

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x+ 4)* 2 f(9(x)) = (2x2 +…

A:

Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

A: A detailed solution is given below

Q: Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements…

A:

Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

A:

Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

A:

Q: Find the partial derivative. z = (x2 + 4x – 2y)° -

A:

Q: 3. Find the area of one of the sine curve.

A:

Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c)…

A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

Q: (7,-2) and Perform the vector operation, given that u = v = (-4, 5). %3D 9. 2u + 3v A-n

A:

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve).…

A:

Q: The following series 2n-1 3n n=1 none of them converges to 1 converges to 2/3 converges to 4…

A:

Q: (D² +6D+9)y=e³* 3x

A:

Q: Find the values of a and b that make f continuous everywhere.

A:

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

A:

Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: We need to find speed at given point.

Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

A:

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

A:

Q: Using the fundamental theorem of calculus, find the derivative of the integral -3x+2 t -dx 1+t3

A: We have to find derivative of given function.

Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral x³Inx A x² dx 3 O ---fa…

A:

Q: nd and of the following equation then simplify whenever possible. dx dx2 x = 3em y = 2mem

A: Given query is to find derivative of the expression.

Q: Find V. (V × F) if F(x, y, z) = sin xi + 8 cos(10x – 11y)j+ 3zk. %3D - V·(V × F) :

A:

Q: 4.)S V dx Use only The Method of substitution/u-substitution on this item. Final answer should be in…

A:

Q: 1. Find the equation of the normal line at a given point. y = - @ (5,1)

A:

Q: dx tan x +sin x+1

A: Solution of the problem as follows

Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

A:

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

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A:

Q: Find the arc length of the graph of r(t) = ev2'i + e-V24j+ 2tk, 0<t< v2 In 9 NOTE: Enter the exact…

A:

Q: Exercises: Imaginary Roots of Auxiliary Equations Solve the equations 1) (D2 – 2D + 5)y = 0 %3D 2)…

A:

Q: Find the partial derivatives of f(x, y) = 5x*y². %3D

A: