Find the linear approximation to sin(x) at the point x-0 and use your answer to approximate the values of sin(.01), sin(.1) and sin(1). Compare your answer with the true values by computing the absolute error.

Q: Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to…

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Q: Find the antiderivative of f(x) = sin^2x

A: Antiderivative=∫sin2xdxsin2x=1−cos2x2So,∫sin2xdx=∫1−cos2x2dx=12∫1−cos2xdx=12∫1dx−∫cos2xdx=12x−∫cos2x…

Q: For what value of t will the slope of a line tangent to x = 6 sin t, y = t² + t be 0?

A: We have to find t

Q: Find the local extrema of the function f(x, y) = e-(cos(r)+sin(y)) and test for which are max, min,…

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Q: Find the length of the curve y = In sin x from t = -2 to t = 0.

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Q: Find the third derivative of f(x) = ³/15z + 1. f"" (2) - ab a b √a |a| π sin (a) 2.

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Q: Consider the equation f(x) = x* + 2x – e* – 3, approximate the root with accuracy up to 2…

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Q: Use a computer algebra system to plot y2 = x 3 - 4x for x and y between -4 and 4. Show that if dx /…

A: y2=x3-4x

Q: to determine the approximate value of v(1+x³)dx

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Q: Find the given higher-order derivative. f (4)(t) = t cos t, f (5)(t)

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Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

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Q: ÿ + ỷ = sec t tan t

A: This is the question of the differential equation.

Q: -Fill in the first 3 levels of Richardson extrapolation to estimate the derivative of sin(x) at æ =…

A: The function given is as follows: fx=sinx We are asked to find the value of the derivative of the…

Q: Find the second derivative of F(t) = | sin(x) cos(2)d.r.

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Q: бл Approximate sin by using a linear approximation with f(x) = sin x. 13 (等) z f(a) + f ' (a)·h = c,…

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Q: Find the linearization of the function y = f(x) = x2 sin(x) at a = π/4 and use it to approximate the…

A: Given,

Q: Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to…

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Q: Compute the derivative of the given function. g(t) = 2t*e' – 4 sin t cos t g'(1) =

A: on doing differentiation with respect to t we get

Q: Find the second derivative of the function. h(t) = 10 cos t − 15 sin t

A: Given: ht=10cost-15sint for finding second derivative of given function, initially we find first…

Q: Use linear approximation, i.e. the tangent line, to approximate 2.9° as follows: Let f(x) x'. Find…

A: The equation of the tangent to the function is given by the formula , The derivative of the function…

Q: Find the actual error when the first derivative of f(x) = sin(2x) at x = T/8 is approximated by the…

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Q: Find the equations of the tangent line and normal lines to the graph of the function f(x) = 3 sin x…

A: Given,  fx = 3sinx  We have to find the equation of tangent line and normal line at x = π2

Q: Find the derivative f (t) = 1- cos t | a. 1 cos t - 1 sin t C. 1– cos t - t · sint (1 – cos t)? b.

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Q: Find the actual error when the first derivative of f (x) = sin(2x) at x = 1/8 is approximated by %3D…

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Q: Find the values of x between 0 and 2n, if any, where the graph of y(x) = sin(x) cos(x) has a…

A: Given : yx = sinxcosx

Q: Differentiate the function.

A: Given: F(t) = et sin 2t  To find: Derivative of the function.

Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: The slope of the normal line to the tangent line of 1 is f(x) = (sin x)² at a = V2 :Select one V2 .a…

A: We have to find slope of normal to the tangent line of fx=sin-1 x2 at x=12. We know the slope of…

Q: For function y implicitly defined by the equation 3 cos(y) = x + 2y + 4, find its linear…

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Q: The slope of the normal line to the tangent line of 1 is 1 f(x) = (sin x)² at a = V2 %3D :Select one…

A: Given:    f(x)=(sin−1x)2  at x=12.

Q: for the function f(x) = 2 cos(45x)o , determine:  the average rate of change for the interval 13  ≤…

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Q: What is the derivative of the following? sin(t) d dt f 117 da cos(t) s(t) 4-sin² (t) 1 4 — sin² (t)…

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Q: The derivative of the function y = cos -1 = COS Va at 1 is equal to 4 :Select one -2 .a V3 .b V3 .C…

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Q: Consider the function f(x) = e^x2−6x+5 . Find the value(s) of x at which the tangent line is…

A: Given thatf(x)=ex2−6x+5ddx(f(x))=ddx(ex2−6x+5)               =ex2ddx(x2) −6               =2xex2-6

Q: The function f(x)=|x|·sin(x) is differentiable at x=0.

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Q: Given f(x) = x-x* + 3x - 2 0, Use Newton's Method to find the root in the interval [1, 2] correct to…

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Q: Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Given that,

Q: The height of an arch above theground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is the…

A: The height of an arch above the ground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is…

Q: (a) Find the slope of the line tangent to the curve y = sin x at the point where x = T/3. (b) Show…

A: (a) we have to  find the slope of the tangent line to the curve y=sin5x at the point where x=π3. as…

Q: Find the slope of the tangent line to the path of a carnival ride x 7 cos() + sin(7t), y = 7 sin() +…

A: Given  x=7cos(t)+sin(7t) y=7sin(t)+cos(7t) We need to find the slope of tangent at t=0

Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: Calculate the error of approximation with Ea for the following functions when x = 2, Ax = dx = 0.08

A: If the input of a function y=f(x) changes, its output also changes. The derivative of a function is…

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A: cos32° It can be written as, cos32°=cos30°+2° Now, fx=cosx, x=30° & ∆x=2°=2π180 radians Now…

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

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Q: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

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Q: For which  x value(s) is the function  f ( x ) = sin ^− 1 ⁡ ( 2 x )  defined and not differentiable?

A: Given that the function is       f(x) = sin-1(2x)  Here we have to find those values of x, in which…

Q: H.W Ex.(8) Show that the functions f(x) = sin' () and ga)=2 tanv メ+) have the Same derivative.

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Q: For what value(s) of x in the interval -15 sxs -5 will the sinusoidal function shown below have a…

A: By definition, a function is a special case of a relation between the members of two sets. It is a…

Q: Find the differential of each function. (a) y = x2 sin(4x)

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