43 31) Describe all y=flx) which are defìned for all XEIR and satisfy continuoUs functions ə47 equation f(x) = flx)

Q: Find the values of a and b that make f continuous everywhere. x2 4 if x 3 a = b =

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Q: Prove that f(x)= 2x-tan^1x-ln(x+√x^2+1) increasing on [0, infinity]

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Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: find I of implicit function sec""cImcy)- In(8**) when yoo

A: 9999

Q: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

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Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

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Q: -x²+5 < f (x) < x+1 2

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: Show that the function is continuous. (x) = 3x cos 3x

A: Show that the function is continuous. (x) = 3x cos 3x

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) = if 2 < x…

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Q: 1 If f(x,y,z)= of then x-y-3-

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Q: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, 1]?

A: follow next step

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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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: Let f: [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution in…

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: If f(x) =- 2-cos(x) sin(x) then the absolute minimum of f on the TI 3T is: interval O 2/2-1 O 2/2+1

A: Steps to find the absolute minimum value : Find the critical point of f Evaluate the function…

Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

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Q: Suppose f(x) = π − 2x − cos x. (a) Show that f is strictly decreasing on R. (b) Hence, justify that…

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Q: 57. Compute the derivative of f(x) = x3/2 using the limit definition. Hint: Show that f(x +h) – f(x)…

A: To show that the derivative of the given function by using limit definition is

Q: If Зх — 2,х <3 -{ - h(x) х4 — 74, х 2 3 Is h(x) continuous at (x=3)? 1 Add file

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Q: 11. Determine the absolute extreme values of the function fx) = 2 cosx- x on the interval 0<x<2x.

A: We are authorized to solve only 1 question, please repost remaining Extrema

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

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Q: Prove that constant function is differentiable at ever x ER.

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

Q: 14. Prove that sin x cos x from dx first principles and be sure to prove all limits used.

A: Proof of limit which is used to prove derivative of sin(x) is cos(x).

Q: (b). Find the bound for absolute error at x = 2.9 on the interval [x, x,], where x, = 2.25, x, =…

A: On the interval x0,xn where x0=2.25, x1=2.5, x2=2.75, x3=3 with n=3 along with the function…

Q: 5) Suppose that f is the function implicitly defined by the equation + tan ( In = evi near the point…

A: Given:       x+y4+ Tanin xy = ey   →1    near the point ( 4, 4 ) eTo Determine: f is an increasing…

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

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Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Show that f (x) =++1 1 - is not uni form continuous on (-1,0)

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Q: 12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if…

A: We have to find critical points and state whether they are maximum or minimum using second…

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: 4. "The function f(x)= x-1 is continuous on(-0,0)". Is the statement true or false? If it is false,…

A: f(x) is continuous at x = a if L.H.L = R.H.L. = f(a).

Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: If f is continous on [0,1) ,then f has absolute minimum on(0,1) True or false?

A: Extreme value theorem says that, if a function is continous on a closed interval [b, a] , then it…

Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: 13 Use the Linear Approximation to estimate Af for f(x): when a = 2 and Ax = 2+x %3D (Use decimal…

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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: Verify Mean Value Theorem for the function f(x) = x in interval [0, 9] %3D

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Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

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Q: Show that cothx x+1 In X-1,

A: Solution

Q: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

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Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…

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.