Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when needed. r(t) = cos(nt)i - In(t)j+Vt – 16k; to = 17 Domain is: Choose one NOTE: Enter your answer in terms of i, j, and k. r(17) = %3D

Q: Evaluate the definite integral (10x + + 3)dr

A: topic- definite integral

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A:

Q: Condense the expression to the logarithm of a single quantity. log (x + 1) + 2 log3(x - 1)] + 6 log3…

A:

Q: Apply

A: We will solve the integration.

Q: Given function:  f(x) = 4x^3 - 7x^2 + 2x - 5 A. Find the exact x & y coordinates of stationary…

A: Given: f(x)=4x3-7x2+2x-5

Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

A:

Q: A- Find Tylor series generated by f(x) = 2* at 1.

A: The given function fx=2x at a=1

Q: Solve the triangle. 3. B. 7. As 38.2° (Round to one decimal place as needed.) (Round to one decimal…

A:

Q: Find Taylor series generated by f(x) = 3x5 -x* + 2x3 + x² - 2, at a = -1 %3D |

A:

Q: Find V x (V x F) if F(x, y, z) = 5xyj+7xyz k. %3D V × (V × F)

A: Curl vector

Q: Show that the function f defined by 1, (x, y) = (1, – 1) f (x, y) : .2 x + y (x, y) # (1, – 1) x + y…

A:

Q: Q1) Determine if the following integrals converge or diverge. If the integral converges determine…

A: Please refer to the image below

Q: Question 3 Suppose C=0, so that 2y 24y 5x3 = 0. Find all points (x,y) at which the tangent line to…

A:

Q: Determine if the following function is continuous or discontinuous at x = 0? 4 +5 f(z) = 9-3z

A:

Q: X+3 Q4) Find the integration by using: J: dx 2x3-8X

A: This question is based on indefinite integral.

Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

A:

Q: Use the half-angle formulas to find the exact value of the trigonometric function sin 112.5°. ...…

A: Use the half-angle formulas to find the exact value of the trigonometric function sin 112.5°.

Q: 2. S(e" + e-3)² dt

A:

Q: chain rule to find given w = x² + 2y² + z² and x = cos (st), y = -2s lnt an 3s2 Vt.

A: We have to find out derivative

Q: dzy What is dx2 for the curve given by x = t2 and y = t3?

A: Our Aim is to find d2ydx2 for the curve given by x=t2 and y=t3

Q: 6x + k, x 4 such a k does not exist O 2 O 4 30 17

A: The given function,  f(x)=6x+k,x≤4kx2-6,x>4

Q: Consider the function f(t) = 6 sec (t) – 6t°. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A:

Q: 1. Differentiate and simplify. a. .2 y = 3x+3x ||

A:

Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula k(t) to find k(t). 13 r(t) = 10 cos(7t)i+ 10 sin(7t)j+…

A: Given; r(t)=10cos(7t)i+10sin(10t)j+3tk

Q: Evaluate the definite integral 6 sin(x)dx

A:

Q: dy then dx If y = In(x/x² + 1), 2x2 + 1 C) x/x² + 1 2a2 +1 D) x(x² + 1) x² + x +1 E) x(x² + 1) 1 A)…

A: Find the derivative

Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: arc length

Q: xp - )s ɛ

A: As per the guidelines I can solve only first question

Q: dg 1+sin 2x Find of g(x) dx 2x-tan 2x

A: To find the derivative of given function.

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

A:

Q: Consider a population of a certain country that is observed to grow exponentially. Based  from the…

A:

Q: 11 a) Use the rational root theorem to find the possible rational roots of 12.r -8r-3T+2=0 b) List…

A:

Q: (d) sec(x) – sec(x) sin²(x) = cos (x)

A:

Q: Find V · (V × F) if F(x, y, z) = 6 sin xi + 6 cos(6x – 7y)j+ 2zk. | V· (V × F) =

A:

Q: Find f andf, and evaluate each at the given point. y' f(x, y) (6, -6) = arctan f,(6, -6) = (6, -6) =

A:

Q: dy when x = 1 is dx If y = e-ª In x then A) 0 B) Does not exist D) = E) e

A: We have to find the dy/dx    at x  =1

Q: To evaluate the Integrals, use the additive Interval property of Integrals which Is glven as…

A: answer is in next step

Q: Fnd the average value of the function over the glven Interval. (Round your answer to three dedmal…

A:

Q: Use the chain rule to find and , where as z = x² + xy + y, x = 6s + 9t, y = 5s + 8t %D First the…

A:

Q: The graph of y= f (x) is drawn below, sketch a graph of y = f(x).

A:

Q: 5. Find the Maclaurin series for f(x) = In(1 Do not use the building block from the previous…

A:

Q: sec(0) = cot(0) = (b) y (1, -1) sin(0) = cos(0) = tan(0) = csc(0) = sec(0) = cot(0) =

A:

Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: Problem No. 1: Evaluate - dx using basic substitution method.

A: First I have used the substitution to make integral easy and then evaluate it.

Q: Find the exact values of the six trigonometric functions of each angle 0. (a) y (-V7, -1) sin(0) =…

A: (a) From the given figure: Here, OA=AB2+OB2=7+1=8=22

Q: 2 ー (4-x²) dx -2

A:

Q: 7. Given that tan (A) = - and angle A is in 3rd quadrant and cos(B) = - and 13 angle B is in 2th…

A:

Q: X+3 Q4) Find the integration by using: dx 2x3-8X

A: