Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

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A: Solution is given below:

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A: Solution : Given that integral is

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Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…

Q: Evaluate lim (x) x-0 f(x) . . . . . . . . . . . F . . y 4 f(x) g(x) X

A: See this solution in below

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Q: Exercises L- If H B =). 33" 3 14. BB+A-SI-D E A-

A: The answer is given below:

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Q: Use Linear Approximation to estimate the quantity 1 80.5

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Q: Step 2 Apply the rule of integration by parts. J u dv = uv - Submit J Let dv = ew dw and integrate…

A: topic- indefinite integral

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A: Volume

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A: Given that y=x3,y=1and x=3, about the line x=3.Using washer /disk mathodr=3-y13r=Radius of…

Q: Given the points A(-6, -5,5) and B( −6, −5, 1). Question 3 a) Write parametric and symmetric…

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Q: 13. Consider the functions f(x) and g(x) in the tables below. 5 6 7 8 f(x) 1 4 2 3 (A) g(x)= -f(x)+3…

A: topic- functions

Q: x+2 3.) (x²-1)(x²+1)² of factor. dx; Solve by using partial fraction. Indicate the type

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Q: Question 1 Let a = 2i - 3j + 2k and b = i - 2j - k. a) Determine whether the vectors a and b are…

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A: Given :fx=1x

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A: The limit is evaluated below.

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A: Let's find slope and y intercept.

Q: Consider the three matrices A = (b) 2 -1 1 0 -1 2 94-1 B = 2 y and C = −1 multiplication is…

A: The objective of the question is determine sizes if possible and evaluate the values x,y and z.

Q: 1. Given the space curve r(t) = (2e¹,e²¹.e^¹), find the curvature at t = 0

A: I am attaching image so that you understand each and every step.

Q: Use the half angle identity for sin² x. sin²(x) Hence, sin² x = ~ √₁² (₁²- V = π (1-sin²(x) 2 sin 2x…

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

Q: the maximum and minimum values of the function f(x) = 6 sin(x) cos(x) + 10 on the interval [0, by…

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Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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Q: compound proposition (PnQ)-(PUQ) is a

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Q: Which of the following describes the graph of h(x) = −3(x − 1)²(x + 1)²(x + 2)? O-12 O -10 -0 -4 -12…

A: see below the answer and explanation

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A: You must have idea how to find distance under v-t curve.

Q: A-Find the intercepts, the symmetry for the polar equation r = cos20 am draw it.

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Q: At what value of x does the local max of f(x) occur? X = ƒ(x) = √² 1²-2 - 25 1 + cos² (t) dt

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Q: performance-enhancing Suppose that a test for drugs is 85% accurate (It will correctly detect 85% of…

A: Given that a test for performance-enhancing drugs is 85% accurate. Suppose that 5% of the 1600…

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A: Given :∫1232xe-xdx

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Q: A graphing calculator is recommended. Consider the function below. (If an answer does not exist,…

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Q: Find the antiderivativef e* sinxdx A.je*(sinx – cosx) + c C. e*(sinx — cosx) + c Find the…

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Q: 3. 3 1 S (2x - 4y)dydx 1 -1

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Q: 2. Find the equation of the line tangent to the circle x + y + 6x - 2y - 15 = 0 at the point (1,-2).

A: x2 + y2 + 6x -2y -15 = 0  given we have to find equation of tangent line to circle  for that first…

Q: III. Use the Laplace transform to solve the initial value problems. (a) y" + 3y + 2y = 0; y(0) = 1,…

A: As per bartleby guidelines we only give first three question answers.  Please repost for other…

Q: At what point (x, y) is the function f(x) = 6x - 6 closest to the origin? Enter an exact answer.…

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Q: Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan A = B 10 Figure 1 A…

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Q: 03/ A. For the following function f(x). Find: ji. iii. m=? 1-4X m -UX.=-u P(1,-1) f(x)=x-2x² The…

A: See this solution in below

Q: The volume of the solid obtained by rotating the region enclosed by y = x = 1, x = 7, y = 0

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Q: P 1. por Find a power series representation for the function f(x) = 92 and determine the radius of…

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Q: 2. Approximate √64.1 by using linearization and use a calculator to compute the percentage error.

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Q: Find the derivative of F(y). Select the correct answer. F( y) = sinh y tanh y F' (y) = sinh y sech y…

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Q: Evaluate the integral. Select the correct answer. O In | csc 4x + cot 4 x | + C sin x + cos x + C S…

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Q: Volume of the function g(x, y)=√64-x² - y² over the semicircle bounded by x² + y² ≤ 64, x≥ 0. 2- -2-…

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