Derive the numerical differentiation formula s'cro) - xo) --4(xo - h) + (xo - 2h) 2h Find the optimum stepsize h that minimize the error.

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: Find the value of the derivative of (z – 4i)8 at z = 3 + 4i |

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Q: Find the tangent line to the function f (x) = x² – 4x + 5 at the point (3,2).

A: To find: The tangent line to function fx=x2-4x+5 at the point 3,2. Formula used: The slope of…

Q: Find the equation of the tangent and normal line of the function f(x) = V2x – 1 at the point (5, 3).

A: fx = 2x-1     , 5,3f'x = ddx2x-1     = ddx2x-112        = 122x-1ddx2x-1        = 222x-1 = 12x-1∴f'5…

Q: 9) Find the equation of the tangent line to the function f(x)=-3x² - 2x at the point where x=1. Give…

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Q: 1. Explain how to use the differentiation part of the Fundamental Theorem of Calculus px 2+sin(4t)…

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Q: Find the equation of the tangent line to the function f(x)=x3−2x2−3x at the point (1,−4)

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Q: az ) Use Implicit differentiation to find ax and for x2 – y2 +z? – 2z = 4 ду

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Q: (18) Verify by differentiation Va? + x² + c. 1 dx x² Va² + x² a²x

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Q: Find the equation of the tangent line to f (x) = ex at x = 2. Give answer in exact form. x²-1

A: Given : fx=exx2-1

Q: Find an equation of the tangent line to f (x) = x² Vx4 – 12 at x = 2. - %3D

A: Explained below

Q: Find the equation of the tangent line to f(x)=xe2x-2 + 3 at the point (1,4).

A: Slope of a tangent of a function at a point is equal to the value of the derivative at that point.To…

Q: First compute y' and y" by implicit differentiation. Then solve the given equation for y, and…

A: xy=y-2

Q: 8. Find the slope-intercept equation of the tangent line to f(x) = 3x² – 4x + 5 at the point (1, 4).…

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Q: Use chain rule of differentiation to find  Y is equal to 3x²-5x +12 X is equal to 2u²-5u +11 Find…

A: Consider the given function asy=3x2-5x+12 And x=2u2-5u+11

Q: What is the equation of the tangent line at 3x+1 (0₁²) of f(x)= ³x + 1 0, 2 X-2

A: Diffrentiation of f(x) is done using product rule diffrentiation.…

Q: Find the equation of the tangent line to f(x)=−2x−4x^−1/2+3 at the point (4,−7).

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Q: By using first principle of differentiation find f'(y), if ƒ(y) = /My – N

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Q: Determine the equation of the tangent line of the given function: f(x) = 3x² – 2x; (-1,5) y = -8x-3…

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Q: Q4 Use implicit differentiation to find an equation of the tangent line to the following curve at…

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Q: Verify the formulas by differentiation. ∫1/(x + 1)2 dx = -1/x + 1 + C

A: Here f(x)=1x+12we have to verify that ∫1x+12 dx=-1x+1+C∫f(x) dx=∫1x+12 dxsubstitute…

Q: ; Find the equation of the tangent and normal line of the function f(x): V2x – 1 at the point (5,…

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Q: Verify the differentiation formula.

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Q: b) Use the method of Differentiation from first principle to prove that the derivative of the square…

A: To prove  ddxx=12xLet  f(x)=x

Q: b) Use the method of Differentiation from first principle to prove that the derivative of the square…

A: Consider the provided information, ddxx=12x Prove that left hand side is equal to right hand side.…

Q: Find the equation of the tangent line to the function f(x) = –3x² form y - 2x at the point where x…

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Q: Find the equation of the tangent line at the given point on the curve. 109y2e 327x/10. (10,3) , 3x2…

A: Given,

Q: Find the equation of the tangent line at the given point. 1 f(x) = х, (-1,2) Vx2 3

A: We have to find the equation of the tangent line of  f(x) = 1x23-x  at (-1, 2).

Q: 1. y, x= 1+ 1+y

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Q: Find the equation of the tangent line to the function f(x) = -3x – 2x2 – 1 at the point where x =…

A: Given : fx = -3x3 -2x2 -1

Q: 3. Find the equation of the tangent line to sin-(x - 2y) = 2ry- 1 at the point (1,

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Q: Write an equation of the tangent line to the curve f(x) = 3x/√x-4 at the point (5,15). Express the…

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Q: By using first principle of differentiation find f'(y), if fV) = My – N

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Q: Find the equation of the tangent line to  f(x) = x2 − 2x + 2  at  x = 5.

A: The given equation is fx=x2-2x+2.

Q: Find the equation of the tangent line to the function f(x)=−4x2−3x+2 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1given

Q: 4. Use three strategies to find in terms of x and y. dx 3x? Given: Strategy 1: Use implicit…

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Q: Find the equation of the tangent line to the function f(x)=−3x3−2x2−1 at the point where x=−1. Give…

A: we have to find tangent line to f(x) at x=-1

Q: Find the equation of the tangent line of the function at the given point. 9. f(x) = 3x+2 (0,-2) x-1…

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Q: Find the equation of the tangent line to the curve g(x) = 4x² – 3x + 2 at the point (1, 3).

A: As we know that; The expression for the equation of the tangent line is: y-y1=mx-x1 Where; m is the…

Q: Find the second derivative by implicit differentiation of 8x2 + 16y2 = 144 at (1, 1)  Choices: A.…

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Q: 3) Using implicit differentiation, find y' if 4x 15xy + 13y 1 %3D

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Q: Find the slope of the tangent line to f(x) = x² – 3x at (-1,4). O 4 O -1 O 2x-3 O-5

A: Given query is to find the slope of the tangent at (-1,4).

Q: Find the equation of the tangent line to f(x)=4x+x^−1/2+1 at the point (4,35/2)

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Q: 6x 2) = 4 y7

A: 2) Given- 6xy7=4 To find- The derivative of the above expression using implict differentiation.

Q: 1. Find the equation of the tangent line to f(x)= 4x2 - 5x+2 at (-1,11).

A: We can find the equation of tangent to the curve as below.

Q: Find the equation of the tangent line of "f" at the given point f(x)=(x-4),(x2+6x-1),(0,4)

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Q: st -xp- 4–lu 1 +x4 y =

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Q: 1. Use implicit differentiation to find all points on the graph of y3 – 3y = 2² + 3r +2 at which the…

A: When tangent is vertical then slope of tangent not defined