ind the linear approximation to the following function at the given point a. f(x) = 4x² + x, a = 4 he linear approximation is L(x) =

Q: Given the linear approximation at a = 0, determine the largest value of such that the 1 linear…

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Q: The velocity in m>s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

A:

Q: If we did a linear approximation of f(x) = = Vx around a = 4 we would find that f(1) is…

A: Given query is to find the linear approximation at a = 4 and x = 1.

Q: Show that g(t) = t / ( t+1 ) takes on the value 0.499 for some tin [0, l].

A: To show that g(t)=tt+1takes on the value 0.499 for some t in [0, 1]. We use intermediate value…

Q: 3 Consider the function f(x)= 2x +1 a. Write the linear approximation to f(x) at x = 4. b. Use your…

A: Explanation of the answer is as follows

Q: Find all values of x where the slope of the tangent line to f(x)=4x^2−3x+2 is 0. x = ___ If…

A: Topic = Derivative

Q: Given f(x)= 1+x. a) Find the linear approximation to f (x) at x=0. b) Use the linear approximation…

A: Since you have posted multiple subparts question in this question so I have solved first three…

Q: HW. Determine the positive root of f(x) = x 10 – 1 using the Newton-Raphson method and an initial…

A: Given: To determine the positive root of f(x)=x10-1  using the Newton-Raphson method and an initial…

Q: The derivative dy of the function y = f(x) with dx f (x) = e' (1ª + 2t³) is a) e' (41³ + 61²) + e'…

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Q: Find the equation of the tangent line ļ to the graph of f at P and x and y the intercepls of L.…

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Q: 1+x (a) Find the approximation of f, dx using Simpson's rule with step size h 1+x2 0.25.

A: The solution is given as

Q: 3. Let f(2) = 1+ 2e" – 3x. At what value(s) of a does f(x) have a horizontal tangent line? Give…

A: Differentiating given function with respect to x, we get

Q: At any time t, the velocity of a particle moving along the y-axis is given by v(t)= 4t - t^2. The…

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Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: tf(x) = e2sinx. Use the local linear approximation of f at x = 0 to approximate e 2sin (0.01)

A: linear approximation

Q: Find linearization of the given function: f(x) = 1/x at x=0.5, dx = 0.1 %3D

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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: Solve the following problems completely. Estimate (1.02) V0.99 using a local linear approximation of…

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Q: (a) Find the linearization L(x) of f (x) = v25 – x² at a = 3. (b) Use the linear approximation L(x)…

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Q: Let f'(z) = tangent line to the graph of the function h(z) = g(13x+3) at e and g(x) = f(/#). Let L…

A: Given, f'x = ex2  gx = fx L is the slope of the tangent line to the graph of function hx = g13x+3 at…

Q: Find the local linear approximation of the function f(x)=Square root of (15+x) at x-subscript 0 = 1…

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Q: t² – 4 - 4 f(x) = -dt 1+ cos²(t) 0.

A: Given:  f(x)=∫0xt2−41+cos2tdt

Q: 1. For f(x) = tan¬1 x: a. Use a linear approximation to estimate the value of f(1.2). Give your…

A: To find - For fx = tan-1x Use a linear approximation to estimate the value of f1.2. Give your…

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: a) Consider f (x) = x³. Write the linear approximation of f for x near 2. Let's call this linear…

A: According to Bartley guidelines first question done....for remaining questions you have…

Q: Use differentials to find the approximate value of y: (2x – 1)* when x = 0.98. O (E) None of the…

A: Given :f(x)=2x-14x=0.98

Q: Find the linear approximation to the equation f(x, y) = 4 ln(x¹ −y) at the point (3,80,0), and use…

A: Linear approximation

Q: Find the linear approximation to f(x) = 1 and then use that to approximate close to 1.003 1 1.003

A: Given: The function fx=1x To find: The linear approximation to fx=1x close to 11.003, then…

Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

A: I am going to solve the given problem by using some calculus to get the required result.

Q: Consider the function f (x) = 3xe* 0 the approximate solution with Newton-Raphson method for 1sxS2…

A: Given function is f(x)=3xex      1≤x≤2 So f'(x)=3xex+3ex⇒f'(x)=3ex(x+1) So by Newton-Raphson formula…

Q: 1. Given the function f(x, y) = x² /ÿ. (a) Find the local linear approximation of f at the point (3,…

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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: The function f(z) = 1 has a poles at z = %3| ez – 1

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Q: 25. The function g(x) = [", |u| du is not differentiable at x = 0.

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Q: Q5/ Estimate the root of the following function using Newton-Raphson method, employing an initial…

A: Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph…

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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Q: Find the linear approximation to the function. x2 f(x + Δx) ≈      Evaluate it at the given…

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Q: Find the linear approximation L(x) of the function g(x) = V1+x at a = 0. L(x) = Use it to…

A: Near 0,

Q: Find the linear approximation, L(x), of at x = 9. Use this to approximate f(11). Do you think your…

A: Let take a function: fx=x The linear approximation can be calculated as: Lx=fa+f'ax-a…

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: The third order derivative of the function y = In(1 – x) - at x = 0 is et O A. Undefined OB. C. 4 D.…

A: As per our guideline we supposed to answer only first question , kindly re post other as next…

Q: 13. Find the derivative of the function T(z) = dz +b cz +d numbers such that ad – bc + 0. When is…

A: Hello. Since your question has multiple parts, we will solve first question that means question (13)…

Q: We previously modeled daylight hours with the function f(t) = 12.13 + 2.77sin(πt/6-1.6), with t…

A: Given: Daylight hours model is given by, f(t)=12.13+2.77sinπ6t-1.6, where t is measured in months.

Q: Find any value(s) of the constant a such that the line y = ax is tangent to the curve f(x) = -x² +…

A: Tangent of a curved touches the curve only at one point.

Q: 24.) Given the function f(x)=x²– 2x Estimate J f(x) dx using four subintervals by . finding R4, L4…

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Q: Solve the following initial value problem for y as a function of x. dy X- 3Dx? -9, х23, у(3)%3D0

A: By using integration formulas

Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: Estimate the solution of the function f(x) 2sin(2x)- 1 using the Newton's Raphson method with an…

A: Given f(x)=2sin(2x)-1 Take the derivative for the function, f'(x)=4cos2x Then the formula for newton…