Let the function f(x) be given as follows: ax + b, x<1 f(x) = ; lt +x + 1, x 21 Employ appropriate technique to find a and b such that the function f(x) is differentiable.

Q: Q5: a- Use two segment trapezoidal rule to integrate the following function numerically: f(x) =…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: : Apply Rolle's theorem for the function f(z) = 7x² – 28z+ 21 over the interval [1,3]. er.

A: The given function is, f(x)=7x2-28x+21 over the interval [1,3]. Observe that, the given function…

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: The function f (x, y) = sin(xy)/xy is defined for xy ≠ 0.(a) Is it possible to extend the domain of…

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Q: Let f(x) = { *, if x= 2 ; for the eax if x + 2 function to be continuous at x = 2 the value of a is

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Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: Let f : R → (−1, 1) be given by f(x) = x/(1 + |x|). Show that f is differentiable at x = 0, with…

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Q: Let f(x) = (x2 + 3x)e .Find the value of c that satisfies the conclusion of Rolle's Theorem for f on…

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Q: Let F (16xyz + 7 sin x, 8x² z, 8x²y). Find a function f so that F f(0,0, 0) = 0.

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Q: Consider the function f(x) = a²e15z. f(x) has two inflection points at x = C and x = D with C < D…

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Q: If f"(x) = V - cos(x). f'(0) = 2, and f(0) = 0, find f(x). %3D

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Q: Differentiate f(x) with respect to g(x) of yx=xsiny

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Q: Show that the function is differentiable by finding values of ε1 and ε2 as designated in the…

A: Given, the function f(x, y) = 5x – 10y + y3, we have to show that the function is differential by…

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: Let f be a differentiable function such that f(4) = 3 and f'(x) = -3x + 3. What is the approximation…

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Q: Let f be a differentiable function such that f (1) = 8 and f' (x) = V2x – 1. What is the value of f…

A: Given data is : f'x=2x-1

Q: Differentiate f(x) 3D 3a-1) with 2+a respect to x. Assume a is a positive constant.

A: (11) The maximum number of beats in one minute: Hx=208-0.7x   The term x is the age of a healthy…

Q: Find the antiderivative F of the function f(x)= x^2 + 2x + 2 such that F(-1) = -1.  F(x) =

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Q: Let be a real function of y=f(x) real variable implicitly defined by the equation 2xy−x2y2+ey=0.…

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Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Find given that z is a differentiable function of x and y, and xz + yz3 = 2 +x²ev

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Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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Q: . Suppose that F(t) is a twice-differentiable function of one variable. Define the function f(x, y)…

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Q: If f(z) is analytic function and u(x,y) = x3 - 3xy find f(z) %3D

A: Given that the real part of the analytic function f(z) is, u(x,y) =x3-3xy To find the analytic…

Q: Find a2z given that z is a differentiable function of x and y, and xz + yz3 = 2 + x²e♥

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Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

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Q: On what domain is the function f(x) = – 4+ v–48 – 6x continuous?

A: The given function is: f(x)=-4+-48-6x

Q: Let f(x) = 2 – x². Over the interval [0, 2], calculate (a) R4 and (b) L4

A: As per the instruction, we will be answering only the first question. For (1), For L4:

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

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Q: Find the interval(s) where f(x)= x²- 2x+3 is continuous.

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Q: Use the definition of differentiability to prove that the following functionns are differentiable at…

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Q: 1. Why is f not a function from R to R if a) f(x)= 1/x? b) f(x) = T? c) f(x) =±V(x² + 1)?

A: We'll answer the first question since the exact one was not specified. Please submit a new question…

Q: Calculate the approximation of My for the given function and interval f Cx)=フメーンLュ,3 %3D

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Q: Suppose that f(x, y) = sin(4x + 6y) is a function of two variables. %3D

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Q: If Tn,0(x) = ao +a¡x+ a2x² +.. he function f(x) centered at x = %3D -) True p) False

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,…

Q: Find the antiderivative F of f that satisfies the given conditions. SHOW WORK!!! 1. 4Vx + f(x) = ;…

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Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: Show the function f(z) = 1+2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

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Q: By using the local linear approximation of the function f(x)=√1+x at x₁ = 0, the approximation for…

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Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: If f(2) = 14, f' is continuous, and f'(t)dt = 23, what is the value of f(5)=? %3D

A: Given :

Q: "The function f(z) = x2 + i(2y + x) is nowhere analytic" is this statement true or false

A: If the function f(z) = x2 + i(2y+x) is analytic then it must satisfy Cauchy Riemann equation. Here,…

Q: If z = y + f(x^2-y^2), where f is differentiable, show that y(∂z/∂x) + x (∂z/∂y) = x.

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Q: Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C…

A: Rolle's theorem: If f(x) is a real-valued function defined on a,b such that; 1). f(x) is continuous…

Q: Use the definition of continuous to proce whether or not the function is continuous at x=5z (F2, D3)…

A: See the attachment

Q: .For what values of a is Jaax - 2a, x z 2 f(x) 12, x < 2 continuous at every x?

A: Here given function  Since,  it is continuous for every x thus it Is also continuous for x=2