Use a plot of f(x) = x* to estimate the value c such that f'(c) = 0. Find c to sufficient accuracy 65. GU so that |f(c+h) – f(c)| < 0.006 for h = +0.001

Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: Use Simpsons Rule to approximate e-x*dx using n = 8 and state a bound on the error. The fourth…

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Q: The derivative of a function f(x) at a particular value of x can be approximately calculated by f(x)…

A: The given function is f(x)=7e0.5x.

Q: Find the approximate value of derivative f′(0) with the step size h for the following function by…

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Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Find the derivative of y with respect to x. 1 y=x' In (x)---x obra d we do O A. 7x5-x² OB. 8x5-x2…

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Q: Proof the n + 1 derivative of xk is zero, where k <n

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Q: What is the approximate derivative of f(x) = x²ex, using backward-difference approach at x=2 and a…

A: The formula for the backward difference is f'x=fxi+1-fxih Now, h=0.1xi=2xi+1=xi+h=2+0.1=2.1fx=x2ex

Q: Given a function f with input that has the dimension [x] = L-M-T-1, such that [f(x)] = L-M, find the…

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

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Q: 5. (a) Use the limit definition of the derivative to find the derivative of f(r) = /5I+1. %3D

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Q: 2) Given: f(x) = x+sin(2x) over the interval (0,7) a) Use a sign analysis to find the relative…

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Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given         f(x)=sin-1x , a=π12

Q: Find the intervals in which the function f(x)=sin (log,x)+cos(log,x)is decreasing.

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: х+1 3.) y = х-2

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Q: 3. The slope of the tangent line to f(x) = A tan(¤) is 1/2 when z = 2n/3. Deter- mine the equation…

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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 the…

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Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: we have been given f(x)=sinx, g(x)=cosx and h(x)=2x. we have to find the exact value of the…

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

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Q: The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate F(x) dx, where…

A: Observing the graph it is clear that the function f(x) is a decreasing function and is concave up.…

Q: Determine the RMS Value of y=root x over the range of x=0 and x=1

A: We have to find the rms value of the given function over the given interval.     This problem can be…

Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: Given function: fx=sinx

Q: 3. Use the formula ((x+h)-f(x) to approximate the derivative of f(x) = 3x² at x = 1 h using h = 0.1.…

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Q: Use forward-difference formula to evaluate the first derivative of y = tan(r) at a = using a value…

A: We know that the forward difference formula is: f'(x)=f(x+h)-f(x)hThe given function is : y=tan(x)We…

Q: 8.) f(x) = v5x* – 12

A: Given:        fx=5x6-12        fx=5x6-1212 differentiating on both sides    f'x=ddx5x6-1212

Q: Q2// Use Euler's method (with all details) to find approximate value of y when x = 3 of = 2y-2x²-3,…

A: The Given initial value problem is: dydx=2y-2x2-3, y(0)=2, h=0.3 To find: y(3) using Euler's…

Q: .Find the estimate for the root of f(x) = sin x+ cos (r+1)-1using Bisection methodx, = 1.5, X=2 with…

A: Solution

Q: The second derivative of the function g is given by g' (x) = 0.1x³ – 0.29xª – 0.694x³ + 1.9136x². -…

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Q: Given the function f(x) = – x° – 6x2 + 5x + 12 , use either the First Derivative Test OR the %3D -…

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Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

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Q: In the interval 3 < x < 4 of the first derivative test, f(x) is a. Not moving b. Changes direction…

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Q: Find the tangent line approximation for f(x) = V2 – x at x = -2. Use it to estimate the value at x =…

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Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: u=ex3 +y2z, where x=p ; y=eq ; z=sin r ; find ??/?? , ??/?? and ??/?

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Q: Use Newton- Rophson Methad to find th Of the equalion in the range Solution ex t x- 10, ex + X -

A: If an equation is f(x)=0, then according to Newton Raphson method: Xn+1=Xn-f(Xn)f'(Xn)…

Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x)=…

A: Solution is below  f'(x0)=12hfx0+h-fx0-h-h26f3ξ1

Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…

A: See the attachment.

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.

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Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

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Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x) =…

A: To approximate the value of the first derivative of the below function at x=2 with h=0.1. fx=xex

Q: 2. Using the definition of derivative, prove the following: 1 (a) f'(x) =E if f(x) = V

A: The given function is  f(x) = x1/3 To find f'(x)

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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