For what value of p will r) be continuous? x-4 for x S2 %3D 2x + 3p for x> 2 f(x) =

Q: If f is continuous on la,b] then | tf(x)dx = f(x)dx 'a A) True B) False

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Q: (c) Suppose that ƒ hits every value between y = 0 and y = 1 on the interval [0, 1]. Must ƒ be…

A: A function is continuous when its graph is a single unbroken curve , that you could draw without…

Q: If f is continuous and f(x)dx=10 on the interval [0,4] find xf(x^2) dx on the interval [0,2]

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: We know,  ln(x) is continuous for all x>0 Polynomial function of x is continuous for all real x.…

Q: If a continuous RV X follows N(0, 2), find P{1 1}.

A:

Q: If f is continuous and f(x) dx = 8, find xf(x?) dx. %3D

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Q: Q3) For what values of a and b are ax + 2b , y =x? + 3a -b, (3х -5, 0 2 Continuous at every x ?

A: Equate at given value

Q: For what values of a is Jaʼx – 2a, x2 2 f(x) ( 12, x< 2 continuous at every x?

A: Given : The function is f(x) =a2x - 2a        , x ≥212,                     x&lt;2 .

Q: If f' is continuous on [a, b], show that 2 f(x)f'(x) dx = (F(b))? – (F(a)² %3D -

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Q: Determine the interval(s) where f(x) = is continuous. 1- In(1/r)

A: It is given that, f(x)=11-ln1/x   A function is said to continuous in an interval in which it is…

Q: a) At how many points is f(z) discontinuous? b) At how many pints is f(z) not differentiable?

A: This is a calculus problem and I solved it in the next step.

Q: Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x 2 Continuous at every x ?

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Q: For what value of b is X - b b + l' x 0 continuous at every x?

A: The given function is gx=x-bb+1if x&lt;0x2+b if x&gt;0. If the above function is continuous at x=0,…

Q: For what values of a is

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Q: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: Iff is continuous on [a,b], then rtf(x) dx = π f(x) dx 1 A True B) False

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Q: If f is continuous and f(x)dx=4, | xf(x?)dx=

A: We will find the value of the integral as following.

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

A:

Q: Let f be a continuous function such that | f(x) da = 13 and 10 3 f(x) dx = 8. What is the value of…

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Q: For what value of b is

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Q: Consider the function F(x) = | s(t) dt , where a is a constant and f is continuous everywhere. By…

A: Find we have to use definition of derivative.

Q: is Continuous and S' fldx=l6, find S xf(x*)a

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Q: For what value of a is

A: Given           f(x)=x2-1    ,  x&lt;32ax       ,   x≥3

Q: For what interval is f (x) = xe concave down?

A:

Q: Find a value of x, if any, at which f (x) = Vx – 64 is not continuous. ff(x)is continuous for all…

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Q: Q3) For what values of a and b are -x* +а, xsin + 1 0<xs y = bx3 + 2 , Continuous at every x ?

A: Explanation of the answer is as follows

Q: For what values of a and b is ах + 2b, x² + 3a – b, Зх — 5, 0 2 |continuous at every x?

A: Given:

Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

A:

Q: For what values of a and b is ax + 26, x? + 3a – b, 0 2 continuous at every x?

A: Given: gx=ax+2b,x≤0……1x2+3a-b,0&lt;x≤2……23x-5,x&gt;2……3   where x is continuous at every point.   To…

Q: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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Q: Q3) For what values of a and b are ax + 2b , y = {x? + 3a -b, (3x-5 , 0 2 Continuous at every x ?

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Q: Given a2 +1, x 1. Is f differentiable at x = 1? Is it continuous at x = 1?.

A:

Q: Q3) For what values of a and b are -х2 +а , x<0 x in+1, 0 < x<- y = bx3 + 2, Continuous at every x ?

A:

Q: Q3) For what values of a and b are -x² + a , x< 0 1 xsin-+1 , 0 < x< y = bx³ + 2 , Continuous at…

A: See the attachment

Q: If ƒ is continuous on [a, b] and, what can you conclude about ƒ?

A: the integral given to us is ∫ab|f(x)|dx=0

Q: B/ For what value of a is fo continuous at every x? x? – 1, x< 3 { fx) = 2ах, x2 3

A: Our objective is to find the value of a for which f(x) is continuous at every x.

Q: Q3) For what values of a and b are (-x² + a , y = { xsin-+1, 0 < xs: bx³ + 2 , Continuous at every x…

A: See the attachment

Q: let X be continuous r.v. with pdf f(x) = kx2 where 0 ≤ x ≤ 1 . Find k then use it to find E(x). What…

A: We have to find value of constant and then mean.

Q: Q: Which c.d.f. F is of X is continuous at x=0?

A: If F(0) = F(0-) then F(x) is said to be continuous at x = 0

Q: - For what value of b is Sx, bx?, x2 -2 x<-2 х, g(x) = continuous at every x?

A:

Q: . For what value(s) of c is f(x) = 54-x³, x < 3) %3D lcx² + 13, x 2 3) continuous everywhere?

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Q: Is the given function f (x, y, z) = xª – 6xy? + 723 continuous at the origin? Yes No

A: If a function f and another function g is continuous at arbitrary point. Then there sum, difference…

Q: If x is a r.v. with c.d.f. F(x), F(x) is continuous at x = 10, then P(X= 10) = 0. True False

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: Q3) For what values of a and b are ax + 2b , y = x2 + 3a -b, 3x-5, 0 2 Continuous at every x ?

A: We will check continuity at breaking points of the function. For continuity , left hand limit and…

Q: Q3) For what values of a and b are (-x² +a, y ={ xsin - bx3 + 2 , 0 <x<: Continuous at every x ?

A: Given information: The function is y=x2+a          x≤0xsin1x+1   0&lt;x≤1πbx3+2       x&gt;1π…

Q: [a, b]. If F(x) is an antiderivative of f(x), for real numbers ¤) + k]dx is equal to

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Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

A:

Q: Find values ofa and b that make B(x) both continuous and differentiable at x = 2: ax? B(x) ={ 6x + b…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.