Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: Prove, using the definition of derivative, that if f(x)  = Cps x,then f'(x) =- Sin x

A: Given fx=cos xBy definition of derivativef'x=limh→0 fx+h-fxhfx=cos xThereforef'x=limh→0 cosx+h-cos…

Q: What is the derivative of 1+x3 at the point (1, )? O 1/4 O- 1/4 O 1

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Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

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Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have;  f(x)=x32

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: Let f(x)=," 1 Use the definition (first principle) to determine the 1-x derivative of ƒ(x).

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Q: 1) Use the limit definition to find the derivative of the function f(x) = 3x – 5x?. Then find all…

A: Derivative of the function in terms of limit is f'(x)=limh→0f(x+h)-f(x)h

Q: 2 The derivative of (g(x))¯ is equal to (g '(x))¯. Select one: True False

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Q: 2) NOT use the short cut method). Use the result to find the slope of the tangent line at the point…

A: Topic:- Derivative

Q: 7 Let f(x) x – 9 * Then according to the definition of derivative

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Q: If the derivative of f is f'(x) = (x – 1)(x + 2), then f is decreasing on (-2, 1) Select one: True…

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Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: 15. If f(x) = x2 - 6x - 9, find f(x) by using the formula/limit definition of derivative.

A: Given: fx=x2-6x-9 we know that derivative for any given functionfx by using limit definition is…

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

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Q: Find f'(x) from f(x)= = 2x³x²x+ 2 using the definition of a derivative. (Do not include "f'(x) =" in…

A: Use simple differentiation formula.

Q: Prove, using the definition of derivative, that if f(x) = cos x then f ' (x) = - sin x

A: we have to prove by using the definition of derivative that if f(x)=cosx then f'(x)=-sinx   as we…

Q: By using the definition of the derivative find to f "(x) 3x3 +1 1 Ve +1 x +1

A: 1. We solve first order derivative of f(x)

Q: Show with the middle value theorem that the second derivative f'′ has at least one zero (for this…

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Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: 1. Evaluate the derivative of f (x)= sec(In(x²)). DO NOT SIMPLIFY.

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Q: 6. Use the definition of derivative to find f'(x) if f(x) 3D х2 — Зх — 4

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Q: Compute for the derivative of the function f(x)= Arctan (csc2 (3x2/3))

A: Some derivative formulas: ddxtan-1x=11+x2 ddxcscx=-cotx cscx Chain rule of derivative:…

Q: Use use the limit definition of the derivative to show that f(x) has the qiven denvative. f(x)= _2…

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Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Use the second derivative test to find the local exterma of the function f(x) =x3+12x2-5 on R

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Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: The derivative and antiderivative of a function are unique. O True False

A: derivative of a function is always unique  but integration is not unique, it depends on constant…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: Find all relative extrema of the function f(x) = x² - 4x² + 2 by using the Second Derivative Test…

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Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

Q: Apply the first derivative test to indentify all relative extrema. f(x) = ¹²-2x+1

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Q: Show that f (x) = 1x-5| is NOT differentiable at 5 by using the definition of the derivative, (Start…

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Q: 4. Use the limit definition of derivative to find f'(x) for f(x) = V5x + 1. You will only get credit…

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Q: 4. By the definition of derivative prove that f(x) = √x² +5 is differen- tiable at x=2.

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Q: By using first principle, show that the derivative of f(x)=- is x+1 1 S'(x) = (x+1)

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Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Verify that the function f satisfies the Mean Value Theorem for derivative. Then fin all values c…

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Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

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Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: If function f(x) is not continuous at the value x = a then the derivative of f does not exist at x =…

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Q: 5л? + 3х — 14 (а) f(*) %3D 5х — 4 6x² + 4/x (b) f(x) = %3D

A:

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: