An object is at the origin at time , with velocity  at that time. The acceleration changes over time, and is given by the function < t2, sin(t), t >. Find the path of the object. Make all necessary calculations, and graph the Path using Maple for .

Q: Find an equation of the tangent to the curve at the given point. x = sin(?t),      y = t2 + t;…

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Q: Find the equation of the tangent line to the curve y = 5x cos T at the point (T, – 57). The equation…

A: Please refer the attached image for complete solution. THANK YOU.

Q: nd an equation of the tangent line to the graph of the function f defined by the equation at the…

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Q: The temperature in Edmonton, over the course of a year, can be approximated using the sinusoidal…

A: The given sinusoidal function is: Tx=16.11sin0.51x-1.75+9.14   ......(1)where T is the temperature…

Q: (a) If F(x) = 12x/(3 + x²), find F '(3) and use it to find an equation of the tangent line to the…

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Q: Let f(x) = 14x + 11 – 3e. Then the equation of the tangent line to the graph of f() at the point (0,…

A: Given: f(x)=14x+11−3ex The equation of the tangent to the graph f(x) at the point (0,8), is given…

Q: B) Find all the points on the curve y=tan x, -n/2<x</2, where the tangent line is parallel to the…

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Q: Find the derivative of the trigonometric function. g(t) = 5 cos2t

A: g(t) = 5 cos2t We need to find the derivative of the trigonometric function:

Q: 5n 3n Find the equation of the tangents to the curve y = sin x at x = 0, x, and . Graph the curve…

A: Given:- y = sin(x)  To find:- Equation of tangent line at point x = 0,π, 5π/2 And graph of f(x) with…

Q: Function Point h(t) sin t + et %D 7 7

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Q: Find the harmonic function which vanishes on the hypotenuse and has prescribed values on the other…

A: prescribed values on the other two sides of an isosceles right−angledtriangle formed by x=0, y=0,…

Q: Find the equations of the tangent line and normal lines to the graph of the function f(x)= —4 sinx…

A: We have to find

Q: 57. Find an equation of the tangent line to the graph of f(x) = x - Vx a) at (1,0); b) at (4, 14);…

A: Consider the given function. fx=x2-x Find the derivative of the function. f'x=ddxx2-x=2x-12x

Q: Consider the function y = f (x) = x² + 9x + 18 and the -value xo = 9. (a) Find a formula for the…

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Q: (x) = 5sinx/6sinx+4cosx The equation of the tangent line to

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Q: A particle is moving in such a way that its velocity v is given by the equation v(t) = cost + sin t.…

A: Given : vt = cost + sint

Q: 2. Consider the function h(x) = 11 - + x3 a) Find the equation of the tangent line to the graph of h…

A: We will find the equation of tangent line as shown below

Q: Consider the function y=f(x)=x²+8x+12 and the x-value x0=9. a. Find a formula for the slope of the…

A: Question is solved.

Q: The graph of 3 (x+y) = 25 (x -y²), shown in the figure, is a lemniscate of Bernoulli. Find the…

A: Given query is to find equation ifbthe tangent at given point.

Q: Find the equation of the tangent line to the curve y = 4 sin x + 2 cos a at the point (0, 1/2). The…

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Q: If f(x) = 3x² – 7x + 2, find f'(1). 3x – 7x + 2 at the point (1, – 2). Use this to find the equation…

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Q: Find an equation of the tangent line to the function y 5x at the point P(1, 5). Solution

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Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: b) Find f(1) and find the equation of the tangent line at the point (1, f(1). c) Graph y = f(x) and…

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Q: Find the equation of the tangent line to the function f(x) = -3x? – 2x at the point where x = 1.…

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Given:f(x)=5x(1+x2) Formula: ddxf(x)g(x)=g (x)f'(x)-f(x)g'(x)g(x)2

Q: Determine an equation for the tangent to each function at the point with the given x-coordinate. 77…

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Q: Find for the function defined implicitly by x?y + ay? = b, where a and dx b are fixed constant. For…

A: The given equation is x2y+ay2=b, where a and b are the constants.

Q: a)find an equation for the tangent line drawn to the graph of f(x)=1/x at x=2. b)Find the exact…

A: a)

Q: If h(x) = 3 – 4x°, find h' (1). = 3 – 4x° at the point (1, – 1). The Use this to find the equation…

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Q: Consider the function y = f(x) = x² + 17 + 72 and the x-value xo = 2 (a) Find a formula for the…

A: Let y=f(x)Then, Slope is given by,                                  m= dydx = df(x)dx

Q: For the given function, find (a) the equation of the secant line through the points where x has the…

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Q: Find the derivative of the trigonometric function.

A: To Find: The derivative of ht=2cot2π t+2

Q: Find the derivative of the trigonometric function. h(t) = 2 cot2( t + 2)

A: h(t)=2cot2(t+2)Here we use the concept of chain rule. Formulas ddxxn=n xn-1ddxcot x=-csc2x

Q: At a certain ocean bay, the maximum height of the water is 4 m above mean sea level at 8:00 a.m. The…

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Q: Given the function f(x)=−2xcos(x), find f′(x). Then find the equation of the tangent line at at the…

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Q: Let f(x) = 6x + 2 – 7e*. Then the equation of the tangent line to the graph of f(x) at the point (0,…

A: Here we find the tangent equation then we find the value of m and b.

Q: If h(x) = 2 – 2a°, find h' (1). Use this to find the equation of the tangent line to the curve y = 2…

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Q: Consider the function y = f (x) = x² + 8x + 16 and the x-value xo = 3. (a) Find a formula for the…

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Q: Find the equation of the tangent line at x =7 for f(x) = 6 – x. Write the answer in the form y= mx…

A: Equation of the tangent at x=7 is y=mx+b where m is slope

Q: Consider the following. Function Point (÷) f(x) = tan? (a) Find an equation of the tangent line to…

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Q: T, and 27. Graph the curve over the interval 2' 3n 3n together with their tangents. Label each Find…

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Q: Find the equation of the tangent line to the curve y 8 sin r at the point The equation of this…

A: Given query is to find the equation of tangent line. Since slope of  tangent is given by derivative…

Q: Find an equation of the tangent line to the graph of the function at the given point. g(x) = ex7 −…

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Q: Consider the function f(x) = x / x^2+9 use the function to complete the following steps:  a.) find…

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Q: Consider the following function. Vx, (1, 1) (a) Find an equation of the tangent line to the graph of…

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Q: Consider the function y = f(x) = x + VT and the x-value xo = 16. %3D (a) Find a formula for the…

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Q: Eliminate the parameter to find a Cartesian equation of the curve, for - くtく æ(t) = 4 tan? t y(t) =…

A: Given parametric equation x=4 tan2ty=-6 sect-π2&lt;t&lt;π2