18. Find numbers a and b so that r+ 4, ux + b, 3r 8, x> 3 1

Q: 8. If f is continuous and f(x) dx 10, find xf(x²) dr. %3D Give proper reasoning.

A:

Q: 3. If f is continuous and | f(x) dx = 10, find af(x*) dr. Give proper reasoning.

A:

Q: Suppose that fis continuous and that / f(x)dr=4 and / s(x) dr=7, Find / 45 (x) dx A 20 B 28 16 12

A: using property∫acf(x) dx=∫abf(x) dx + ∫bcf(x) dx∫-33f(x)dx +∫36f(x)dx=∫-36f(x) dx4 + ∫36f(x)dx…

Q: Suppose that f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) = 3, and f" is continuous. Find the value of *…

A: Use the method for integration by parts to solve the integral.

Q: Is the following bounded or unbounded and why? f(x,y) = ln(x2 + y2)

A:

Q: 46. Find the values of a and b that make ƒ continuous everywhere. 4 - if x < 2 f(x) = ax? if 2 <x <…

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Q: Suppose f(1) is continuous everywhere, and has the following values: 10 20 30 40 f(z) -4 9. 11 3. 7…

A: Given,  f(x) is continuos everywhere  f(x) has the following valuesx010203040f(x)-491137To…

Q: As the fun ction Leay) xy js Continuous I+ x*+y? e (-1, 2)

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Q: 6. Suppose that ƒ is differentiable on (a,b). interval [a, b]? Justify your response for find a…

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Q: Show that x is continuous everywhere. r(x)-x-0 XX<0

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Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: 4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and…

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Q: Suppose X is continuous with f(x) = x/2 from 0 to 2. What are the values of f(1) and P(X=1)? 1/2 and…

A: Given,f(x)=x2 ; 0&lt;x&lt;2

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

A:

Q: Suppose that f is continuous and that f(z)dz = 0 and f(z)dz = 7. Find | 5f(x)dx. %3D - - 2 - 2 2 ОА.…

A: Given, ∫-25f(z)dz=7 To find -∫255f(x)dx

Q: Suppose that f (1) = 2 ,f (4) =7, f '(1) = 5, f '(4) = 3and f" is continuous. Find the value of ∫1…

A: Given f1=2f4=7f'1=5f'4=3 f''x is continuous To find value of ∫14xf''xdx

Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: 4) Suppose that f(il=3, F(4) =7, f'W= 3 f'(4)=5 and f" is continuous. Fiod the value of (4 xf "(x)…

A:

Q: 5. Use Green's Theorem to evaluate f. $ (y² – 4x) dæ – (2+ x²y²) dy where C - - is shown below. y…

A:

Q: Suppose that a continuous function g satisfies: 9(z)dr = 42 and 9(2x)dz = 12. | z9(32°)dz. Find

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Q: Show that x| is continuous everywhere. r(x)- x- 0 xX <0

A: f(x) is continuous, if LHL=RHL=f(x&gt;0), where LHL is left hand limit while RHL is right hand…

Q: 2. Find the values of the constants a and b for whichf is continuous everywhere if ax + b, f(x) =…

A:

Q: (2х + 6, хS \x² + 3, x > Finition of continuity. f(x) =

A: Given,                  f(x) = 2x+6x≤0x2+3x&gt;0Now,                LHL = 6 And        RHL = 3Here,…

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

A:

Q: iii If the discontinuity of ƒ is removable, redefine ƒ so that it's continuous at 0

A: This question related to the topic continuity of real analysis.

Q: Suppose that f(1) = 4,| f(4) = –6, f' (1) = 6, f'(4) = 3, and f" is continuous. Find the value of 1…

A: Given: I=∫14xf"xdx, f1=4, f4=-6, f'1=6, f'4=3 For evaluating given integral, we will use integral by…

Q: : Let g : R → R define by 3x for x E Q Then g(x) 2x – 3 for x € Q' :the point where g is continuous…

A: Let f be a function. The function f is said to be continuous at the point c if it satisfies the…

Q: A. is definiteand continuous, B. is indefinite and continuou C. is discontinuous and definit D. is…

A: Given: To explain the correct option of the given statement as follows,

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) 4 10 8 5 5…

A: f(x) is continuous everywhere and has the following value: x 0 10 20 30 40 f(x) 4 10 8 5 5

Q: 50 if x E Q 1 if x € R\ Q Let f(x)= Prove that y=f(x) is not continuous at any points a E IR.

A: Take p ∈ Q and let (xn) be a sequence of irrationals converging to p. Then f (p) = 1 but f (xn)→ 0…

Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

A: To Determine: fins a and b so that the function is continuous and differentiable given: we have a…

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

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

Q: Suppose f is continuous ont he closed interval [a, b). If F(x) is an antiderivative of f(x), for…

A:

Q: Suppose that f(1) = 5, ƒ(4) = -8, f'(1) = 4, f'(4) = -2, and f" is continuous. Find the value of |…

A:

Q: 2x, ifx BDU G EDU y = 5, if x= 3 if x = 3 (x-5, if x 3

A: Given:   y=2xif x&lt;35if x=3x-5if x&gt;3 To prove whether y is continuous or not x=3. Solution: A…

Q: Suppose that  f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 5, and f ''  is continuous. Find the value of…

A:

Q: Let f = f(x, y), x = s +t and y = s - t. Show that (9- ) - se se as at ax ду

A: It is given that, f=f(x,y), x=s+t and y=s-t. Show that, ∂f∂x2−∂f∂y2=∂f∂s·∂f∂t.…

Q: Answer the following statements true or false. 8.1 The sum of continuous functions is continuous.…

A: Here we have to state whether the statement is true or false.

Q: If |fn(x) – fn(y)l 0 and all x, y in a compact interval, show that {fn} is uniformly…

A:

Q: Find the values of a and b that makef continuous everywh x2 – 4 - if x 3 a = b =

A: A function f is continuous when x=c is the same as saying that the function's two-side limit at x=c…

Q: 3. If f is continuous and | f(2) dr = 10, find | af(x*) dr. %3D Give proper reasoning.

A: It is given that if f is continuous and ∫09f(x)dx=10 We have to find ∫03xf(x2)dx=?

Q: 1. Show that if u = x – y, v = y, then for any continuous function f, -" f(r – y, y)dydæ e=s(u+v)…

A:

Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

A:

Q: Suppose f(x) is continuous everywhere, and has the following values: 10 20 30 40 f(x) - 2 7 10 - 4 7…

A:

Q: For what values of a and b is ax + 2b, g(x) = {x? + 3a - b, 0<xS2 3x 5, %3D - continuous at every x?

A: The given function is gx=ax+2b,        x≤0x2+3a-b,  0&lt;x≤23x-5,           x&gt;2. For the given…

Q: Suppose that f (1) = 2, ƒ (4) = 7, f' (1) = 5, f' (4) = 3, and f" is continuous. Find the value of…

A: Given data: f(1)=2 f(2)=4 f'(1)=5 f'(4)=3 The objective is to find the value of ∫14xf''(x)dx Apply…

Q: Show that if u = x – y and v = x + y, then for any continuous f, -2sx * f(x – y, x + y)dydx = / |…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.