Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate the value of sin(2) and sin(15). Compare the approximated values to the exact values.

Q: The linear approximation at x = 0 to sin(2x) is A + Bx where A is: Preview and where B is: Preview

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Q: Let y = tan(4x + 6). Find the differential dy when x = 3 and dx 0.1 %3D Find the differential dy…

A: Explanation is given below...

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A: Given; ey+cosx=1 at point (π/2,0).

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Q: Find the differential of the function. y = 04 sin(120) dy =

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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 differential of the function. y = (2+cos?)1/2 dy=?

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Q: 4 - Find the direction A in which the function f(x, y) = x cos y + y sin x decreases most rapidly at…

A: We have to find the direction A in which the given function decreases most rapidly.

Q: Let y = tan(2x + 3). Find the differential dy when x = 1 and dx = 0.1 Find the differential dy when…

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Find the derivative of the function. cos a y = sin x (1+ v³)® dv

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Q: Find the differential of the function. y = x4 sin(12x) dy = ?

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Q: 5. Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given parametric equations are, x=t3+cosπt, y=4t+sin2t+6. Find the equation of the tangent to…

Q: The linear approximation at x = 0 to sin(3x) is A + Bx where A is: Preview and where B is: Preview

A: Given function:

Q: Let y=tan(2x+6) Find the differential dy when x=1 and dx=0.2 Find the differential dy when x=1 and…

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Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

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Q: Let y = tan(4x + 6). %3D Find the differential dy when x = 5 and dx: 0.4 %3D Find the differential…

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Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: Find the differential of the function. y = 0 sin(60) dy =

A: To find the differentiable of the below function. y=θ3sin6θ

Q: The linear approximation at x 0 to f(x) = sin(6x) is:

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Q: Consider y3-2x2=1+sin(xy)   a) Use implicit differentiation to find dy/dx.   b) Find an equation…

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

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Q: Let y = tan(3r + 5). Find the differential dy when x = 3 and da = 0.1 Find the differential dy when…

A: Here we need to use chain rule of differentiation to find dy. According to chain rule,…

Q: Find the differential of the function y=2x2+3x+1 at the point x=1 when dx=0,1.

A: To find the differential of the given function at point x = 1 when (d x) = 0, 1.

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Q: Let y = tan(4x + 3). Find the differential dy when x = 3 and da Find the differential dy when x = 3…

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Q: 53. df = (x+ 1)ye"dx + xe*dy

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Q: Find the linear approximation to h(y) = Sin(y+ 1) at y =0 Use the linear approximation to…

A: This is a problem of linear approximation.

Q: Find the differential dy of the given function.    y = x tan x

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Q: Find the differential of the function y = V1+ cos(0)

A: Find the differential of the function

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

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -5x – (sin(x))² dy =

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Q: Let y = tan (2x + 6). Find the differential dy when x = 4 and dx = 0.2 Find the differential dy when…

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Q: 1. Determine the equation of the tangent line to the graph of f(a) = [² pr+sin r = x = 0. cos (t² +…

A: Above equation of tangent is given.

Q: Let y = tan(3x + 8). Find the differential dy when x 5 and dx = 0.4 %3D Find the differential dy…

A: First differentiate then put the values

Q: Find the differential dy of the given function Y=arctan(x-5) Dy=?

A: Use the standard derivative of inverse trigonometric function and chain rule.

Q: Let y = tan(4r + 8). Find the differential dy when a = 4 and da = 0.3 Find the differential dy when…

A: Differential equation: - A differential equation is an equation that contains the derivative of an…

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: Find the derivative of the function. - c() (수 1 - e9x 1 + e9x y = cos y' = 18e9z sin + e&= )…

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Q: The derivative of the function y = cos VI at z = is equal to 4

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Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

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Q: Let y = tan(3x + 4). Find the differential dy when x = 4 and dx = 0.4 Find the differential dy when…

A: We know that, ddxtanx=sec2x We have,  y=tan3x+4 On calculating derivative with respect to x, we get…

Q: Let y=tan(3x+3). Find the differential dy when x=5 and dx=0.3  Find the differential dy when x=5 and…

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Q: Find the differential of the function. y = 6 sin(60) dy

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Q: Let y = tan(4x + 5). Find the differential dy when x = 5 and dx = 0.1 %3D Find the differential dy…

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Q: Let y = tan(3x + 8). Find the differential dy when x = 3 and dæ = 0.1 Find the differential dy when…

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Q: Find the differential of the function. w=2xyexz dw=(__)dx + (__)dy + (__)dz

A: W = 2 x y e xz dw  = 2 yexz  + 2 x y z e xz dx  dw  = 2 xe xz dy

Q: Find the differential of the function   y = θ3 sin(6θ)

A: Solution :-

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: