Question no 1: If the given function is continuous and having a root in [-1, a] where a= (last three digits of registration no as 1.23) f(x) = e°cos x)

Q: QUESTION 4 A half range periodic function is defined by f(x) = TTX - 0≤x≤ , f(x) = (x <x<T <X

A: It is frequently essential to acquire a Fourier expansion of a function for the interval (0, p) that…

Q: Question 12 10 If f is a continuous function and F'(x)= f(x) for all x E R, then x)dx=? 2[F(10) –…

A: We have to solve the problem

Q: PART C QUESTION 1 Differentiate the following functions with respect to x: а) y = e3* cosh (x?)

A: The objective of the question is determine the derivative of the given function.

Q: Question 1. Use the Mean Value Theorem for the function log(1+2) over [0, t] to show that for 0…

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Q: QUESTION 4 Let f (x, y )= In (ex+ y) be a function. At which point the function is discontinuous? O…

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Q: Problem 2: (Exe. 18 p. 124) Use the definition of continuity and the properties of limits to show…

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Q: Question 18 Find the critical number(s) of the function. y- 3x +30x Select all that apply. 30 0. 3.…

A: We are authorized to solve only 1 question, please repost remaining questions Critical number

Q: Question 15 Given the function f(x) =4x- 39x2+90x +2 which of the following describes its absolute…

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Q: Question:2 Find domain of following functions S(x, y) = In(e*+e") arctan(x+y) а. f(x, y) = b. ( x² –…

A: The function in a will not be defined when x+y=0.  Thus, domain is:

Q: Question 5 The following function is homogenous of degree what? Vx?y²+x²+y² f(x,y) = х, у ху 1 3 4…

A: We have to find the degree of function.

Q: Question 5:Find the value of constant c, if f(x) is continuous at x = 2 |cx? + 2x if x 2 -

A: Given that: f(x)=cx2+2x    if x&lt;2x3-cx      if x≥2

Q: Problem 1. At what points (if any) is the function continuous? Prove your answer using the 8 – e…

A: f(x)=x, x∈ℚ0, x∉ℚTo Find: At what points(if any), the given function is continuous.

Q: 8. Sketch at least 2 cycles the following function: f(x) = -2 sin [3(x -)) +2 Amplitude: period:…

A: To find- amplitude, maximum and minimum.

Q: Question 9 1-COSX Find k so that f(x) D 4x2 is continuous at x-0 k, x=0 口 1/2 口 2/5 O 1/8 3/4

A: We're going to solve

Q: Question 14 Given the functionf(x)= 4 determine the interval/s at which f(x) is continuous. x+1…

A: f(x)=4x+1Note :If multiple question are given we have to answer only one question .if you want other…

Q: Question 11: Let f(x) = |- x +7|-|-3+x|, where r E R. Let Z = {x: f(x) > 0} . Give explicitly the…

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Q: Question 6 Sketch a continuous function with the following properties: The domain is [0, 4] Ax) > 0…

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Q: Question # x² in tems of Evaluate ( Beta) B function

A: The given integral is: ∫01x21-x512dx

Q: Question no 1: If the given function is continuous and having a root in [-1, a] where a= (last three…

A: ----------------------------------------------------------------------------- False position…

Q: Question 2 Consider f(x) = 1/x on (0, 0). Show that for any a e (0, o0), the area of the triangle…

A: 2 Consider              f(x)=1x    on   x∈(0, ∞) For any,  a∈0, ∞ we have to show that the area of…

Q: Question 4 Consider the function f(x) = -5x – 11x + x? +2x 3 2 smallest number n such that f(n) (x)…

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Q: Question 2. Consider the function f(x) = 1 – x² on [-1, 1], and a point a e [-1,1]. Consider the…

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Q: Question 20 Let f(x) =cos(3x) & g(x) = e . Which of the following is true. (f+ g)(x) = 2 e2x +…

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Q: Question 1 Specify and sketch the domain D(f) of the following function sin(x + y) Va2 – y² + 1 f(x,…

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Q: Question 7 <. Let f(x) = 5 – 8x + 3x. Calculate the following values: f(a) = %3D f(a + h) = f(a + h)…

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Q: Let f be a periodic function with period 3. If f(a-1)=-1, f(a)=0, and f(a+1)=1, what is the value of…

A: It is given that, the function (f) has the period 3. And,

Q: Question:2 Find domain of following functions In(e*+e") а. f(x, у) arctan(x+y) x2 – y? if (x, y) 2)

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Q: Question 4: If you are given f(x) as follows: 1 if x -2 2 Show that f(x) is continuous at x = -2 ?

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Q: QUESTION 2 Use the definition of differentiability to show that the function f(x, y) = cos(x² + xy)…

A: Given function: fx,y=cosx2+xy Function fx,y is differentiable at x0,y0 if: ∂f∂xx0,y0 and ∂f∂yx0,y0…

Q: Question 11 a / f(x) dx: f(x) dx a True False Question 12 If f'(a) = 0, then the function f must…

A: Here we have to use the concept of integration and derivatives.

Q: Question 2. Consider the function f(x) = 1 – x² on [-1, 1], and a point a E [-1,1]. Consider the…

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Q: Question 4 , x5 A -4 B 3 C none of the given choices (D E

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Q: Question 2 Consider f(x) = 1/x on (0, 0). Show that for any a E (0, ∞0), the area of the triangle…

A: We have f(x)=y=1x     , x∈(0,∞)dydx=-1x2for a∈(0,∞)x=a, y=1a, dydx=-1a2

Q: Question 17 sin Given: f(x) = {¹, if x #0 2T if x = 0 What should be the value of k so that f is…

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Q: Question 4: If you are given f(x) as follows: if x -2 2 Show that f(x) is continuous at x = -2 ?

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Q: Question no 1: If the given function is continuous and having a root in [-1, 0.33] f(x) = e* cos x)…

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Q: Question 2. Choose a e R+. (a) Let f: [1, 00) → R be defined as: log(t) f(t) := tl+a Show that there…

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

Q: QUESTION 17 The derivative of f(x)=2x2 +3 if a=0 O AX 2h O an 4h O O

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Q: Question 4. Continuity Exercise 2.5, Problem 26 a. Show that f has a removable discontinuity at x =…

A: We have to show f has removable discontinuity at x=3 and find the value of c

Q: Question 25 Which of the following functions yields the derivative cos 3x g'(x) = 5+2sin 3x g(x)…

A: We know derivative are opposite to anti derivative of function  so i find anti derivative of given…

Q: Question 15 Given ƒ (2) - This function is discontinuous at the point A O z=0 x = -2 O=12 O == 2 <…

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Q: Question 16 Suppose that g(1) = 0 and g is continuous on R. Let f(x) = (x – 2)(x – 3)g(x). Then the…

A: Suppose that g(1) = 0 and g is continuous on R. Let f(x) = (x - 2)(x - 3)g(x). Then the equation:…

Q: Question 4. Let f(r) = e² and g(x) = sin x. Find composite functions f (g(x)) and g(f(x)) and give…

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Q: Question 6 Indicate if the following statement is TRUE or FALSE. Briefly justify your response with…

A: I have given the answer in the next step. Hope you understand that

Q: Question 22 x + 2, x<4 Consider f (x) = { cx + d, 4 < x < 6. x? + 3, x 26 Determine the values of c…

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Q: Question 2 If a function f is continuous at 0, show that g(x) = f(x) is differentiable at 0 and find…

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Q: Question 8 Suppose that H is a function of r satisfying H'(0) (1+-). N H" (r) – aH'(r) = 0, H'(0) =…

A: Given second order homogeneous differential equation : H''r-aH'r=0, where H is a function of r. To…

Q: Question 4 Consider the function k with domain R, k"(t) = A(e - 4e) and A negative and real. Show…

A: Given that:k''(t)=A(e-t-4e-2t)

Q: Question 18 Which of the following functions is not continuous on the interval [0, 3 f(x) = ²³16 Oh…

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Q: Question 8 of 10, Step 1 of 1 Let h(x) = √√x + 5. Find the function given below. h(4n+ 9), n >…

A: Let hx=x+5To find the value of the function given below.h4n+9=?where n≥-72