Find the unit tangent vector T(t). r(t) = (5 cos t, 5 sin t, 2), Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization.)

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r'"(t). 5,3K r(t) = t²i - 4tj + 3. %3D (a) r'(t) (b)…

A: Vector

Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

Q: Evaluate the line integral | -ydx + xdy along the curve C : y? = 18x from (18, 18) to (0,0). NOTE:…

A:

Q: Find y': y arcsin Oy =-- %3D Oy = - zV-9 %3D Oy = %3D zV-9 %3D -69

A:

Q: 2. A turns 100 RPM and B 150 RPM as shown; they are connected by rolling cones. Calculate the cone…

A: Solution: wa = 100 rpm wb = 150 rpm

Q: Sins 느 x Uos

A: We need to evaluate integral.

Q: A ball is kicked such that its height (h) can be represented by the equation h = - 16t2 + 64t + 9,…

A:

Q: S- 3 dy 3y - sin –+C 4– 9y2 3 A True B) False ||

A:

Q: In 1 decimal place Find the Surface Area generated by rotating the first quadrant portion of the…

A:

Q: A function is defined as f(x) = x3 - x - 11 = 0. Between the interval [2,3] find the root of the…

A:

Q: g(x) f(x) - sin(2²) dt, find f(x). = J

A: To Find: f'(x)

Q: lim (1+ sin(18a))/(2«) (A) e? (B) eº (C) e18 (D) ∞ (E) 1 we the question carefully edited 8:11 PM /

A:

Q: Determine the vector field of F. F(x, y) = yi - xj

A:

Q: Use power series operations to find the Taylor series at x = 0 for the following function. x -2+2…

A:

Q: In 1997, researchers at Texas A&M University estimated the operating costs of cotton gin plans of…

A:

Q: 5. [sin-' x dx Ans. x sin'x - V1-x² +

A: We will use integral by parts to evaluate integration of arc sinx

Q: 4х Consider the function A(x)=2x+ for x > 3 Зx-1 (a) This function has one critical value larger…

A: We will start from critical points and follow upto inflection point

Q: 1. The study of integrals in calculus is motivated by the problem of calculating (a) the slope of a…

A:

Q: Find curl (4z i+ 5x j+ 9y k). curl (4z i + 5x j + 9y k) = ( Di + ( j + ( i i )k

A:

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

A: Using Euler's Method we have  xn = xn-1 + h  yn = yn-1 + h . f(xn-1, yn-1)  In the given question we…

Q: 2. Find the Area bounded by the curve y=4-x2 and the x-axis.

A: 2. The area bounded by the curve y=4-x2 and the x-axis Note:    Multiple questions are given, we are…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 6 cos(t)i +6 sin(t)j+…

A: As we know that; The expression for the curvature; κ=r't×r''tr't3 And The expression for the radius…

Q: sec" /x dx 17. 2 5n Ans. 6

A:

Q: Find div F and curl F if F(x, y, z) = 4y®z°i – 11a°z°j – 5xy'k. div F= curl F=

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Find r(t) · u(t). r(t) = (7t – 4)i + j + 4k u(t) = t?i – 8j + t?k r(t) · u(t) = Is the result a…

A: Use dot product concept

Q: æ = (f+ a)soɔ Which among the choices is equal to the dy/dx? In your sc - cos(r+y) A)

A: Given: cos(x+y)=x

Q: Evaluate: 3 A 1–x*) 2 + C 3 (1-x*) ² + C --(1-x*) ² +C D 1-x*) 2 + C 3

A:

Q: Find the area of the loop. Round to 5 decimal places. Technology only for the integral. Do not…

A:

Q: The most conveneient way to evaluate x2- by substitution is to let Vx2- 4 =y A True B) False

A:

Q: Sx+11x+2 dr x(x+1) Zln|x| + 3 In|x+ 1| +C 2łn]x| + 3 In|x +1|- Option 1 Option 2 2ln|x] + 3 Inx+ 1|…

A: We can solve this as follows:

Q: Two numbers have a sum of 72. What is their product if it is a maximum? (A) 1296 B) 1297 c) 1298…

A:

Q: Find sin 0. 4 e in quadrant IV cot 0 = sin 0 = (Simplify your answer, including any radicals. Use…

A:

Q: Find V · (V × F) if F(x, y, z) = 7 sin xi + 10 cos(4x – 5y)j+ 5zk.

A:

Q: 2. sin 2wcos 2wchw

A:

Q: dx V25 – x

A: Given problem:-

Q: Given the function, x = 3 + Vx? + y² , find y. Vx² +y² - X y Vx² + y? - > ア= y Vx? + y² + x ア= y Vx?…

A:

Q: Is the solution region bounded or unbounded?

A:

Q: 1+2x2 dx J x2(1+x?)

A: A detailed solution is given below

Q: Find curl (7z i + 8x j+4y k).

A:

Q: y = [log(arc cot r3)]cosh

A:

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 6 cos(6x – 7y)j + 3zk.

A:

Q: 11 ti + dt

A:

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 30x from (30, 30) to (0,0). NOTE:…

A:

Q: Calculate the flux of the vector field through the given surface. F = zi + 2xj + 3yk, and S is the…

A:

Q: Find the derivative, dy/dx: y = log3 (2x +1) Oy =- (2z+1)3 In 3 Oy = (2r+1) In 3- Oy= log, e (2z+1)3…

A:

Q: Solve

A:

Q: 2. y = [log(arccotx³)]coshx. Find dy/dx

A:

Q: Use power series operations to find the Taylor series at x= 0 for the following function. 17x e* The…

A: we want to find taylor series of the function 17 x ex  about  x=0

Q: In an extensive study of cost functions for 40 firms in Great Britain, it was found that if a is the…

A: