e sin (e^) cos" (e*) c 6. COS

Q: Evaluate the definite integral. e141 i + ej +t k )dt O e14 – 1 1 Li+ (e- - 1) j+, k 14 (e4 – 1) i-…

A: Definite integral

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

A:

Q: 12 Given: F : =â, determine F•â. 2

A: r→=xa^x+ya^y+za^zr=x2+y2+z2a^r=r→r

Q: [3 Compute the matrix exponential e4t for the diagonal matrix A =

A: Given,  A=3004

Q: ||r(t) x r"(t)|| ||r'(t)|³ Use the formula k(t) to find k(t). 13 r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk…

A: A detailed solution is given below

Q: A hot air balloon rising vertically is tracked by an observer located 7 km from the lift-off point.…

A: topic - application of derivatives

Q: Suppose that f is a continuous function such that | f(z) dz =-12. Find 2i (r") dz.

A:

Q: at x = 2 for the function below. dx Evaluate y = - 5u? + 4u + 9, where u = 9x2 – 2x + 4 Answer…

A:

Q: Find the arc length L of the graph of r(t). r(1) – ittj Vor? k. 1 r(t) = t i+tj 2 <t< 5 L = i

A: To find the arc length L  of the graph of r(t).

Q: Since f'(x) is a function, f'(x) has its own graph, one that is based on the behavior of f(x). True…

A:

Q: ||r(t) × r"(t)|| Use the formula k(t) to find «(t). r(t) = e*i+etj K(t) =

A:

Q: What is the difference between contanity? Unforly contanity ?

A: This question is from real analysis &amp; our topic is uniform continuity .

Q: Fin volume of the object formed by rotating f(x)=1/x about the x-axis on the domain 1<x<infinity.…

A: We have to find the volume of the object.

Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

Q: .3 dx

A:

Q: Q2) Solve the D.E xdy + (2y-x+ 3x)dx 0

A:

Q: Differentiate the function. g(u) = 7u + V 5u

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Find the domain of r(t) and the value of r(to).

Q: 16. Interpretations of Integrals Determine the position function, s(t), of an object if the…

A:

Q: 6x7 – 5Vx + 3x + 4x-2 dx

A:

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = 4 cos(7t)i+4 sin(7t)j+ 3tk K(t)…

A: By using the formula kt=r't×r''tr't3 to find kt.rt=4 cos7t i+4 sin7t j+3t k

Q: Integrals

A:

Q: Find S(sin20cose + cos30)d0

A:

Q: Find the average value gave of the function g on the given interval. g(x) = 3x, [8, 64] gave =…

A:

Q: 1. Use a suitable substitution to evaluate , (G) dx. Give you answer correct to at least 2 decimal…

A: Substitution is done for the function whose derivative is present in the numerator.

Q: Find the producers' surplus at a price level of p = $59 for the price-supply equation below. p= S(x)…

A:

Q: Suppose that 2 < f '(x) < 3 for all values of x. What are the minimum and maximum possible values of…

A:

Q: Evaluate the definite integral. ra?/3 xVx6 + a2 dx (a > 0)

A:

Q: (rece - tan 0) de 2. J]

A:

Q: Question The piecewise function f (x) is graphed below. Use geometric formulas to evaluate the…

A:

Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

A:

Q: Consider the region bounded by x = 3y and x = y^2. A solid is formed by rotating the region about…

A: We have to set up the integral to find the volume.

Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: Evaluate: S(4sin (x) – 3sec? (x)) dx

A: ∫ 4sinx-3sec2xdx=∫ 4sinxdx-∫ 3sec2xdx=-4cosx-3tanxAdd a constant to the solution=-4cosx-3tanx+C

Q: Let p= -x - 2x + 20 be the demand function, where p is the unit price of a certain commodity, and z…

A: We have to find the quantity and consumer surplus.

Q: Describe the graph of the equation. (8 – 21) i + 13rj r = O It is a plane in 2-space through the…

A: In this question we have to find point and nature of given vector.   Option d is correct.

Q: Find the arc length of the graph of r(t) = ev2ti+ e¯v2tj+ 2tk, 0<t< v2 In 5 NOTE: Enter the exact…

A:

Q: 8. Given 8. dx = 16 and f(x) C g(x) dx = -5, evaluate the following. %3D (a) [F(x) + g(x)] dx (b)…

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

Q: 3 2. (8x2 – 3x) (12x2 – 3) dx

A:

Q: Evaluate the limit tan x lim z0 2x

A:

Q: What is the absolute maximum value of f(z) = z³ – 3z² +4 on the interval (-1, 1]? %3D (A) 4 -2 (C) 0…

A:

Q: 2. Find the coordinates of the centre, vertices and foci of the curve with parametric equations: x =…

A:

Q: If f(x) = 4x(sin I + cos I), find f'(r) -| 4x cos(r)- 4z sin(r) +4 sin(r) +4 cos(r) f'(1) =

A:

Q: Q3) Evaluate triple integral f, (x2 -y²)dz dx dy.

A:

Q: Determine whether the sequence is convergent or divergent. If it converges, find the limit. {n² tan…

A: Here we have to check the convergence of the sequence.

Q: Find an equation of the plane. The plane through the point (7, 8, 1) and with normal vector 3i +j -…

A:

Q: Find T(t) and N(t) at the given point. r(t) = (t² – 8)i + tj; t= 8

A: Given,            rt=t2-8i+tj ; t=8To find : Tt and Nt at the given point.We know that,…

Q: D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Given that     D(x) = -3x/10 + 8     S(x) = x/5 + 3

Q: A line passes thru (3, 4) and cuts a right triangle with the coordinate axes in the second quadrant…

A: Suppose the line is: xa+yb=1 where a and b are the x and y intercepts respectively. Now, it passes…

Q: 3. Find the absolute maximum value of the function f(x)=- 1+x2

A: