Find the local quadratic approximation of f at x = x0, and use that approximation to find the local linear approximation of f at xo. Use a graphing utility to graph f and the two approximations on the same screen. f(x) = sin(6x), xo = 12 Enter Approximation Formulas below. Local Quadratic Approx = Local Linear Approx =

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Q: Find the first and second derivatives of the function. g(t) = 2 cos t - 3sin t

A: We find the first derivative

Q: Find the first and second derivatives of the function  G(t) = 2 cos t - 3 sin t

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Q: Find the derivative of the function. y = sin−1(3x + 1)

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Q: Q3: i) Find the derivative of the function of y = (x² + 1)sin 3x %3D (ii) Find the absolute maximum…

A: Given:  i) y = x2 + 1sin3x ii) f(x) = x2-13, -3≤x≤3

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A: The function f(x)=sin(x)-x reach height -2

Q: 3. Given f(x)=2x +3x-1 find f'(x) then find the equation of the tangent line to f(x) at (-3,8).

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A: Given: f(x)=sin(2x)+17 To find: f'π2 and f'(π)

Q: Q1 (a) Use partial differentiation to determine the expressions for in the following cases: (i)…

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Q: a) Find the first derivative of the followings: i) f(x) = sec²x tan/x ii) f(u) = cos²(sin(1 – u)-1)…

A: We have to find out the derivative

Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

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A: Given,

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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

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A: The given function is f(x)=1+x at x0=0 we have to Find the local linear approximation.

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Q: 30 Find the real and imaginary parts of the functions (a) z²e2= (b) sin 2z Verify that they are…

A: We will use standard techniques.

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Q: g(x) = Find the derivative of the following function. x, - /V5+? dt Solution Since f(t) = V5 + t2 is…

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Q: Q1 (a) Use partial differentiation to determine the expressions for in the following cases: ôx (i)…

A: Explained below

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A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

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A: Given that: f'xi at xi=0.5△x=0.5, △x=0.25,fx=5x3-cos2x The objective is to determine the errors.

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Q: e derivative of f(x) = 6. (x² + 15x) is | O -6x 3(2x + 15) O 6x + 90- O -6x 2(2x + 15) O 6x 2(2x +…

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Q: let a>o be a fixed real number. Let acoscx?3+ X ln cy) = y2+2xy+ & -1 find the equation of the…

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Q: 3. Let f(x)= 3 cos x-4sin x+5 a) Determine the exact slope of f(x) at a: 4 %3D Зл b) Determine the…

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A: Given function L(x)=f(0)+xf'(0) and differentiable at x=0

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Q: Find the derivative of the function at Po in the direction of A. f(x.y) = 5xy- 5y", Po(-7,-2), A= -…

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Q: the function given below, find the critical points and classify the critical points using 2nd…

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Q: x d) f(x) = x² sin - R e) f(x) = x+₂ x-2

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Q: (c) Use fzero to find when the derivative of 5. S(x) = 9. cos(x) sin(x) is 0 in the interval (0,…

A: NOTE: As per the guidelines we are supposed to answer only one question because all parts or…

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A: We have to find out derivative

Q: Find the derivative of the function at Po in the direction of A. f(x,y)=-3xy + 5y², P₁(-10,2),…

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Q: Consider the function f (x) = x² -4 sin (x) 1. To use Newton Method, what will be the derivative of…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = 2xy + y, Po(-5,10), A= -…

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Q: Q 1. a) Let y = x® – 5x³ + 5x* – 10. Then find minimum and maximum values. b). By using definition…

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Q: f(z) = In(x² + 3) Find the derivative and evaluate it at x = -4. – 4. %3D f'(– 4) = Preview Find a…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1.06 as follows. Let f(æ) = VT and…

A: Solve the following

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A:

Q: The derivative with respect to x of | (3Vi-1) dr is 3x – 1 by the 2nd fundamental theorem of…

A: Given that,         ∫3x3t-1dt

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: