11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

Q: 2. Express in indicated derivative in terms of the function F(r). Assume that F is differentiable.…

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Q: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

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Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

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Q: 6. Find the tangent line to the function f(x) = 2x cos"(x) (0, 1).

A: To find the slope we need…

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: 7. Find the equation of the tangent line (in the form y = mr+b) for the function f(x) = In(x-3)+6V…

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Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: Find the fourth derivative of f (z) = 37 + In(z) – 164z. Enclose arguments of functions in…

A: To Determine: find the fourth derivative of the function .  Given: we have a function…

Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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Q: 2.) Compute for the derivative (DO NOT USE THE DEFINITION) of A. 2x3 y = tanh sin x2

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: 8. Find the point of the graph of f (x) = xe-2x where the tangent line is horizontal. %3D

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Q: ) Find the equation of the tangent line ETL for f(x) = x³ - 2x +1 at x = −1

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Q: 2. Use the definition of the derivative to find f'(x) and f"(x). a) f(x) = x? %3D

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Q: 1. Show that a frination fiłamb ]->1R is differentiable at xolamb) is and only if its lower and…

A: Solution: f:[a,b]→ℝ is differentiable at x0(a,b). Let us take upper derivative at x0+. Then,…

Q: 2) Let f(x) = x' +x² – 5x – 5. Use the second derivative test to classify the critical points.

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Q: The tangent line to y = f(x) at (0, –8) passes through the point (7, 4). Compute the following. a.)…

A: Given: y = f(x) at (0,-8) Passes Point ( 7,4)

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

Q: Prove that f (x) = x3 − 12x is differentiable. Compute f'(x) and findan equation of the tangent line…

A: For a function f(x) to be differentiable the limit limh→0f(x+h)-f(x)h must exist. This limit is…

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: 2) Find the point(s) at which the graph of f (x) = has a horizontal tangent. x2+1 %3D

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Q: The slope of the tangent line to the graph of the function y= Ttx- cotx at x=0 is O T+1 O T-1

A: Solution is given below:

Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is…

A: It is given that the slope of the tangent line to the differentiable function f at the point 2,f2 is…

Q: 2. Find the slope of the tangent line to f(x)=V4-V+5 at the point where x 4.

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Q: 2. Prove that f(x) = |x + 1] 1| (−1,0) tangent line at has no

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: 3. Express the derivative of f (x) = Vx as a limit of the difference quotient ("h → 0")

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Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

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: Suppose for sume function f we heve its derivative, f'cx) = e*sin(x), on the %3D interval o< x< ar.…

A: fx is a function such that f'x=exsinx on the interval 0&lt;x&lt;2π We have to determine where the…

Q: 3. Use the forward-difference formula to approximate the derivative of f (x)=sin(In x) at x, = 2.5…

A: The derivative of the function can be calculated using the difference method. The formula for the…

Q: The tangent line to y=f(x) at (1,-3) passes through the point (3,9). Compute the following: f(1)=?…

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Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: 2. Determine the points on the curve f(x) = sinx-cosx, 0≤x≤27 where the tangent line is horizontal.

A: Find out the points where the tangent line is horizontal.

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: 7) Use a tangent line approximation with the function g(x)= Jx to estimate V9.2

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

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: II) By using the limit definition of derivative, prove the identity J dzf(2)8' (2) = - / da f…

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Q: Find the fourth derivative of f (z) = 57 + In (z) – 109z. Enclose arguments of functions in…

A:

Q: (b) Show that the function defined by √₂²+y f(x, y) = 0 if (x, y) = (0,0) is not differentiable at…

A: On solving this we will get

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

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Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…