Confirm the approximations by using the linear approximation at x = 0

Q: Find the gradient of the tangent line to y when x = 2.

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Q: Find the length of the curve x = 49 sec* t – 1 dt with 3 - - 6. Length is

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Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: The equation of the tangent line to f(x) = 5x2 + 7 at x = 0 is a y = 5x + 7 b y = 7 y = 2x + 14 O d…

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Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

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: Let y = sin(5x). If Ax : = Ay ~ = Find the percentage error error = 0.2 at x = 0, use linear…

A: Linear approximation of y=f(x) at x=x0 is L(x)≈f(x0)+f'(x0)(x-x0)

Q: Let y=sin(2x). If Δx=0.4 at x=0, use linear approximation to estimate Δy.

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Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: In what direction is the derivative of ƒ(x, y) = xy + y2 at P(3, 2) equal to zero?

A: Consider the function and solve.

Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: Find f (3) and f' (3), assuming that the tangent line to y = f (x) at a = 3 has equation y = 5x + 2.

A: Tangent to a function at a point is a line which just touches the graph of the function at that…

Q: Find the derivative of the funciton F(x) = dt. F'(x) =

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Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

Q: Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

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Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

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Q: Estimate the indicated derivative by any method. x = 4t + t2; estimate ds/dt | t= -2

A: Given, x=4t+t2 We have to find dxdt at t=-2 We will use following formula to differentiate the…

Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find the values of x where y = x 3 and y = x 2 + 5x have parallel tangent lines.

A: Parallel lines are the lines that have equal slopes. To find the slope of the tangent line at a…

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

A: Here is the solution

Q: y" +6y' +10y=0; y(0) = 2, y'(0) =

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Q: Estimate the slope f'(3.5) for f (x) = sin(3x) using: a. Forward difference approximation with h =…

A: f(x)= sin3x x y y1 y2 y3 y4 3.3 -0.1557             -0.193       3.5 -0.3507   0.0139…

Q: Use linear approximation (or differentials) to estimate the given number. 3 а. V8.12

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find f(3) and f'(3), assuming that the tangent line to y = f(x) at a = 3 has equation y = 5x +2.

A: Consider the provided function, y=5x+2 Find the value of f3  and  f'3 at a=3. y=5x+2 We can write…

Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: Find f(4) and f' (4), assuming that the tangent line to y = f(x) at a = 4 is y = -6x + 2. %3D

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Q: Evaluate the derivative So (3t² – 2t +1) dt. -

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Q: Differentiate.

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Q: ) Find the equation of the tangent and normal lines of f (x) = x* + 2x at x = -1.

A: Given:

Q: Let y=sin(4x).If Δx=0.2 at x=0, use linear approximation to estimate ΔyΔy≈   Find the percentage…

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Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

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

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Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: To use differentials to approximate V8. You would use x = and dx

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Q: Let y=sin(5x)y=sin(5x). If Δx=0.1Δx=0.1 at x=0x=0, use linear approximation to estimate Δy and find…

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Q: Find all (x,y) points where x² +4y² +4x- 8y+4 = 0 has horizontal or vertical tangent lines.

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Q: 3r %3D 5r + 2 – 1 (d) f(x) =

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Q: dy Compute the derivative y' dt 2t – 9 - y = 5t 2

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Q: 4. Find the Linearization of f (x) sinx at a Provide your answer as L(x) =?

A: The given problem is to find the linearization of the given function at given point. Given…

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the…

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Q: find the degree of Precition @F(x)= X

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