The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line. a(t) = 2t + 2,    v(0) = −3,    0 ≤ t ≤ 3 (a) Find the velocity at time t (b) Find the distance traveled during the given time interval.

Q: a) Graph the function f(x)=x² + 2x b) Draw the tangent lines to the graph at the points whose…

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Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: Use the given velocity function and initial position to estimate the final position s(b) Round to…

A: Given,  v(t)=3(1-e-3t)

Q: Use AMNP, as needed, to complete the given parts. 18 cm 15 cm h cm 16 cm Part 1: Part 2: Part 3:…

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

Q: d d Calculate #ri(t) - r2(t)] and [ri(t) × r2(t)] first by differentiating dt dt the product…

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Q: 2. Consider the following table of a periodic function h(t). t 0 1 2 3 4 5 h 4.0 5.25 6.165 6.5…

A: hmin =1.5hmax=6.5A)Midline:y= hmax+hmin2y=6.5+1.52y=4B)Amplitude:A=hmax-hmin2A=6.5-1.52A=2.5

Q: Find f''(x). 1(x) = (x² + 1)² f''(x) =

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Q: Q4: Find the derivative of the function at P。 in the direction of A 2 1) f(x, y) = 2xy-3y², P (5,5),…

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Q: Question 7 of 8 View Policies Current Attempt in Progress Find the limit. NOTE: Enter the answer…

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Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: How to determine whether the function is continuous or not at a given point x = a ? x ≤ 1 (3x5 - 1…

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Q: Find the average rate of change of f(x) = 5x²-9 on the interval [2, t]. Your answer will be an…

A: Use the formula for the average rate of change of a function.

Q: Find the derivatives of the following function (a) y=4²+2√²

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Q: Find each limit, if it exists. 6-7x (a) lim (b) (c) 000 11 x-∞ 6x³ 6-7x lim x- 6x-2 6-7x² lim x-00…

A: Part a,Given,            limx→∞6-7x6x3-2

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

A: We have to estimate the error in computing the length of the hypotenuse.

Q: Q2: find dw/dt at given value point for the following function 1 1) w = x² + y², x = cos(t), y =…

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Q: Find the Laplace Transformation of y" +3y + 2y - 4ex when y (0) = 0, y′ (0) = 3 OY (s) 2s+1…

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Q: 1 Given f(z) find the average rate of change of f(z) on the interval [10, 10+h]. s z+5 Your answer…

A: The function is given by fx = 1x+5 To evaluate: The average rate of change of the function on the…

Q: Round your answer to four decimal places, if necessary. Approximate the area under the curve on the…

A: We have to find the area by right endpoint rule.

Q: Write the equation of a sine or cosine function to describe the graph. 3- 3 1 π - 4 4 -2 -3 r k | 2

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Q: Current Attempt in Progress Find the exact arc length of the curve .x = 1 = = √ ( ₁² + 2) ²/² ₁ +…

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Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

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Q: Find the arc length of the graph of NOTE: Enter the exact answer. L = r(t) = √2ti + e-√2tj + 2tk,…

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Q: b. √ ( 3 √ √x + ²) a dx

A: The given integral,      ∫3x+1xdx

Q: 3) f(x, y, z)=x² + y² -2=²+ = ln(x). (1,1,1) -1/2 4) ƒ(x, y, z)=(x² + y² + =²)¯¹¹² +ln(xyz),…

A: 3)    fx,y,z=x2+y2-2z2+zlnx We have,       grad∅=∇f=i∂f∂x+j∂f∂y+k∂f∂z ∂f∂x=2x+zx ∂f∂y=2y…

Q: Question 5 Given the function: 5x 6 x < 0 ƒ(z) = { 5x 12 x 20 Calculate the following values: f(-1)…

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Q: c) 59 ² + √x dx x

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Q: Consider à = (2,1,k), and b = (k,-8,k). Find the value of k such that å and bare perpendicular.

A: We can find the values of k as below.

Q: owin - y" −4y' +4y=0 L".

A: 1)  y''-4y'+4y=0 Auxillary equation is m2-4m+4=0m2-2m-2m+4=0m(m-2)-2(m-2)=0(m-2)2=0 ⇒m=2,2

Q: Draw the graphs of the given functions. Find their points of intersection. Find the area bounded by…

A: Given

Q: 9x²-6 2x²-x²-8x+4 B D + x + 2 mx + n None of the choices 4 To evaluate A x-2 A 9 B 3 E 2 S + -dx…

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Q: [CLO-21 f(x) and g(x) are functions that are continuous on the interval -3 ≤x≤2 and satisfy 1…

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Q: Find the laplace transform of f(t) = 21² +41 - 5 F (s) = F(s) = O O -5s² + 4s + 4 53 -555 +454 45³ -…

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Q: Locate the absolute extrema of the function on the closed interval. (a) f(t) = ₂, [3,5] (b) f(x)=…

A: The given functions,a) ft=tt-2, 3,5b) fx=x3-12x, 0,4

Q: An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it…

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Q: 6. Using a double integral, find the area that is inside the region bounded by r = 3+2 sin and r =…

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Q: Solve for the limit of the following limits functions. Write your answers in simplest forms. If the…

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Q: 12. 13. 14. √2+6-√√6 Т lim I-0 LIMIT VALUE: lim 2-1 LIMIT VALUE: Т lim 3 2-8 V 11-2z LIMIT VALUE:…

A: limx→a f(x) =L if and only if limx→a+ f(x) =limx→a- f(x) .

Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ||ti + 1²3|| dt =

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

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Q: Find the laplace transform of f(t) = 2t¹-3e³t+10 cos 2t

A: Given that,  f(t)=2t4-3e3t+10 cos2t

Q: 1. Use the graph of y = f(x) given below to find the answer to each of the following. You do not…

A: By using the graph of y=fx given below to lisy all the intervals on which f is increasing.

Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 17°,…

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Q: 21. Find 1² [f(x) + 28(x)] dx if [²₁ f(x) dx = 5_ and ₁8(1) g(x) dx = -3

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Q: Determine whether the integral is improper L' (x-4)-¹dx (A) Not improper (B) Improper

A: We can solve this as follows:

Q: 18. In each part, evaluate the integral, given that f(x) = (2x, x≤1 x>1 2, (a) forex f(x) dx (b)…

A: 18.fx=2x,x≤12,x&gt;1

Q: 1 (s² + a²) (s² + b²) a sin at + b sin bt a² - b² b sin at a sin br - ab (b²-a²) cos at + cos bt…

A: This question can be solved using the concept of inverse Laplace transform.

Q: Part 1 of 5 - Part I Given the set X = {x € R³ : d(x,a) <r}, where d is the usual metric on R³. A…

A: A set is closed iff its complement is open. So a set is not open iff its complement is not closed.

Q: the slope intercept equation of a line that passes through (0,-6) and (3,-4) is

A: Given points are (0,-6) and (3,-4)and here (0,-6) is (x1,y1) and (3,-4) is (x2,y2)We know the slope…