(a) Find values of the constants m and n that will make the function f continuous everywhere on its domain. m + In(x + e³) x < 0 f (x) = ecos r 0 < x < 3 n + cos-(x – )

Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 4 sin 5x. - 00 0, u(x,0) =…

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Q: Xn Xn=3-(-1)" Xn = cos (¹) √1+n² Xn= 2n-5 Xn = where (yn) is bounded 4 Xn = n(1 + (-1)") + n ¹((−1)"…

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Q: Can you please answer this question and show all of the steps and say the correct letter

A: Consider the limit

Q: Discuss limit(n →∞)fn on B and C for  fn(x)=x/n; B=E1; C = [a, b] ⊂ E1 fn(x)=(cos x + nx)/n; B=E1

A: Note: Since you have not mention anything about the set E1, We are considering it any sunset of real…

Q: x* + x3 x2 +1 플+미2+11+ tan-1 x*C C In x + 1| + tan-1 x +C 3. 쪽-1n x2 + 11 + tan-1x +C D In Jx2 +1| +…

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Q: (1) (x²+2x) dx = (3 - In x²) dy separable exact linear in x linear in y homogeneous Bernoulli in x…

A: Note: As per guidelines of Bartleby we have to solve one question at a time kindly repost remaining…

Q: 4. Let g(x) = [ sin(r² – e*) dx. Compute gʻ(x). g'(x) = sin(x² – e") cos x 5. Let h(x) = S sin(x² –…

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Q: 1) Find the value of m that makes m a) f(x) =- continous at x=0 tan x- sin x x>0 b) Show that the…

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Q: If f (x) is an invertible, differentiable function with tangent line y = 4 x + 7 at the point (0, 7)…

A: we have to swap variable for finding the inverse function

Q: Let f be a differential function defined on the interval (-1,1). Which of the following statement(s)…

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Q: Problem 63

A: Given:

Q: 2(3 + (4 - 1) - 0(1 + (« - 1) Given Ln + (i – 1)- , express the limit as n → 00 as a definite…

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Q: Consider the fourth-order boundary-value problem p'' (x) – a*@(x) = 0 p(0) = p'(0) = 0 P(1) = p"(1)…

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Q: 1) A function f (x) can be linearized around x provided that 8x is very small f (x + 8x) = f (x) +…

A: Topic:- function

Q: 1) A function f (x) can be linearized around x provided that 8x is very small f(x + 8x) = f(x) +…

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Q: Problem 3. Show that the function cos(n²r) f(x) = 2n n=1 is differentiable on [0, 1] and f'(x) is…

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Q: Solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint:…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x = %3D A O 1 .BO -2 .CO 2 .D O 0.

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Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: 2. xp- X2 a. b. + C с. + C d. None of the above dx 3. x(1+x) In xin (1+x")+C b. xarctan (1+x')+C a.…

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

Q: Problem 3. Show that the function cos(n²x) 2n f(x) = Σ n=1 is differentiable on [0, 1] and f'(x) is…

A: Given :  f(x) = ∑n=1∞cosn2x2n To show :  f(x) is differentiable on 0, 1 and f'(x) is continuous on…

Q: 1847 In x 5)- b) Show that the ode (x + tan-¹ y)dx + y dy = 0 is exact, then find the general…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 32. In Example 4 of Section 1.2, we examined how CO2 concentrations (in ppm) have varied from 1974…

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: Differential Calculus Exercise Problem #1 Let f be a function satisfying the following properties:…

A: Asymptotes are the line which tends to touch the function curve but never touches it. Asymptotes…

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 1. Find the particular solution to y' = 3sin(x) given the general solution is y = C - 3cos(x) and…

A: Topic - differential equations

Q: Let k be any real constant. Prove that the function F:R->R satisfies the differential equation…

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Q: For the function f(z) = a pole of order 1 an essential singularity a pole of order 0 a removable…

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Q: Q 42

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Q: 2. A particle moves along the x-axis so that at any time t > 0, its acceldration is a(t) t = 0, the…

A: Given,           at=32cos2t

Q: 15. f(x) = for every x E (-4,3] x+4 16. f(x) = sin (2) in the interval x 2-2 3 17. f(x) = { 2 - x2…

A: As per our guide lines we are advised to solve only first question. Please kindly upload other…

Q: Question 44

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Q: and that there is a deleted neighborhood U of 0 su and n 2 0. Define f(x) = x -4g(x)(1 – cos x) for…

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Q: 35. [T] lim sin2x; ±0.1, +0.01, +0.001, +.0001 *40 X X -0.1 -0.01 -0.001 -0.0001 sin 2x a. b. d. X…

A: The answer is given below:

Q: Question 38 The critical point of f (x) = (sin x) (cosa) on the interval (0, π/2) is at x = Ono…

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Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: b- Compute the roof of the function f(x) = cos(x) +2 sin(x) + x². Please use xo = 0 and x1 = -0.1 as…

A: 4) Instead of x1,x2,x3 I choose variables x,y,z a)

Q: 5. Given that f: [0, 1] →R satisfies If(z) - f(u)| < |x - yl for all r, y € (0, 1] with z#y. Can We…

A: As per the guideline, I would only do the number 5. Kindly repost the other question separately.…

Q: Given Ln 8 = = [(1 + (6 - 1) =) *co ( 7 + (1 - 1) ²)] Σ (i (i (i (i n a = b definite integral, that…

A: Explanation of the answer is as follows

Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: 2. Given g '(x) : 8 – 2x and g is continuous on its domain of (0,0), find the critical values of g.…

A: The objective is to find the critical values of g.

Q: If f(x) = x + 2 cos(x), 0< x < 2n, then f has a local maximum at A) x = 6. B) x = 6 11п C) x = 6. D)…

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Q: Graph f(x) = -2 sin x, g(x) = sin 2x, h(x) = ( f + g)(x) in the same rectangularcoordinate system…

A: fx=-2sinx,  gx=sin2x  &amp;  hx=f+gx When x=0, f0=-2sin0  &amp;  g0=sin20⇒f0=0  &amp;…

Q: J arctan x dx A C In(x2) + C In(x² + 1) + C x arctanx x arctan X - | 1. x arctan x +- In(x2) + C x…

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Q: Let k be any real constant. Prove that the function F:R->R satisfies the differential equation F'=kF…

A: In order to prove a statement of the form " P if and only if Q" , first prove If P then Q and then…

Q: A violin string produces a vibration u(x,t)=a sin(2t-x/ 137). cos(A-t)+b sin(14t-x / 137). cos(E-t)…

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Q: f(x) = 3 x4-4 x3-12 x2+1, has local minimum at x= 1 40 2.80 .CO .DO 0.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.