For Exercises 43 and 44, sketch the graphs of f and ƒ ° f. 2, -4 < x < -1 -1

Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: For Exercises 43 and 44, sketch the graphs of f and fo f. -x - 2, -4 sxS-1 43. f(x) = 1, -1 <xs1 1…

A: 43. f(x)=-x-2-4≤x≤-1-1-1&lt;x≤1x-21&lt;x≤244. f(x)=x+2-2≤x&lt;0x-10≤x≤2

Q: Please show step-by-step solution

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Q: In Exercises 17–20, the linear function. use the limit definition to calculate the derivative of

A: Given:  k ( z ) = 14 z + 12.   To find: The derivative of k ( z ) using limit definition.

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Q: The set of all points where the function f(x) = x |x| is differentiable is (A) (-∞, ∞) (B) (-∞, 0) U…

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Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Find the linearization L(x) of f(x)=tan x at x=3pie/4.

A: Given

Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: Determine the limit of f(x) as x approaches 2. * 51 f(x) 4- 5 4 2 -i 0 i 2 3 4 5 1- -2 3 5+ 3 1 DNE…

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Q: For Exercises 43 and 44, sketch the graphs of ƒ and ƒ  ƒ.

A: (43) Find the value for f(x) at x = -4, -1, 1 and 2.

Q: Number 32

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Q: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

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Q: use graphical approximation methods to find the point(s) of intersction of f(x)=e^x and g(x)=x^6 to…

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Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Q.1. Apply three steps of steepest descent to f (x) %3D 2(х,2 + х?2) +x;x, — 5(х, + х2) with initial…

A: The function given is as follows: fx=2x12+x22+x1x2-5x1+x2 The initial point given is x0=1-2. We will…

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

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A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: . Determine, using full algebraic justification, the exact global minimum point of: f(x) = e*(sinx +…

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Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

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Q: Find the linearization of the function at a . f(x) = sin x    , a = pie /6

A: The given function fx=sinx, a=π6

Q: Find the absolute extrema of the function on the closed interval.

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: What is the largest vertical distance between the graphs of the functions y=√x and y=x 2 in the…

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Q: Find f'(x). f(x) = ex – 2x f'(x) = e-2 %3D Compare the graphs of f and f' and use them to explain…

A: Given  f(x)=ex-2x

Q: Find a and b so that the function S4z - 3x² + 4, z -2 is both continuous and differentiable. a = b =

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Q: Sketch the graph of a continuous function y =f(x) that satisfies the following conditions: 1. f'(x)…

A: This question is about graphing a function

Q: Use the definition of f'(x)=lim/(*+h)-J (x) to find the derivatives of h (а) h0 f(x)=x²-x+2.

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)5 on the interval [0, 4]? Justify.

A: we will see how to proceed

Q: Determine the set of points at which the function is continuous. F(x, y) - х-у 1 + x² + y2

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Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

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Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: In Exercises 41–44, determine if the piecewise-defined function is dif- ferentiable at the origin. S…

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Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: 4- х, хS0 10) Determine if the function y(x) =- 3x, is differentiable at x = 0. X>0

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: x+ (х,у) # (0,0) f(x,у) — 1-/x² +y² +1 k (х, у)%3 (0,0)

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Q: Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and…

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Q: What is the lower limit and upper limit bounded by the curves y 9 - r2 and the line y = x + 7 ? -2…

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Q: The set of all points where the function f(x) = i-e¨ is differentiable is (A) (0 , ∞) (B) ( –0, ∞)…

A: We find the set of all points where the given function f(x) is differentiable.

Q: Exercise 25. For which x- values does the graph of y = e3a-2a²-4x has a horizontal tangent line?…

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Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: For exercises 5-7, use the derivative rules to find f '(x). 5. f(x) = 2 + Vx³ - 3x5 %3D PM Mon Feb…

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Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

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Q: 3. Let # 0, 0, r = 0. f(x, y) = Find f.(x, y), fy(x, y) at all points. Leave your answer as a…

A: We need to find differentiation of f(x,y) with respect to x and y.

Q: Describe the x-values at which f is differentiable. Sx2 - 5, x 0 10 -1 0 1

A: Here, the given function is: f(x)=x2-5, x≤05-x2, x&gt;0 which is a piecewise function.