X+3 fx) 2 X-3x-18

Q: f is continuous iff f-1(E) is closed

A:

Q: For what value of b is             continuous at every x?

A: To find the value of a such that given function is continuous for every x. f(x)=a2x-2a,    x≥212,…

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

A:

Q: Pe A- IF ax +b Continuous at x-1 %3D X+2 and Fca)=3,. Find the Value of Constant a, bER

A: Since the function is continuous at x=1, so the value of the two pieces of the piecewise fucntion…

Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

A:

Q: Let A be a cut. Show that if r ∈ A and s /∈ A, then r &lt; s. To dispel any suspense, let’s get…

A: Consider the definition for the Dedekind cut A.

Q: If f(1) = 2, f(4) = 7, f'(1) = 5, f'(4) 3, and f"(x) is continuous, what is x f"(x) dx? %3D

A: Given: f(1)=2f(4)=7f'(1)=5f'(4)=3I=∫14xf''(x)dx=?

Q: For what values of b is b + 1' x? + b, x > 0 8(x) = continuous at every x?

A: Now we check the continuity at x = 0:

Q: Find fx for f(x, y) = In(x – y).

A: Given that fx,y=lnx-y To find fxx It can be found by fxx=∂2f∂x2     =∂∂x∂f∂x

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

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Q: Find the values of x, if any, at which fis not continuous if f(x) = ² x x+4 A. 0 B. -4 C. 0 and -4…

A: topic - continuity

Q: If f: X →Y is continuous and E C Y is closed, then f-(E) must be: - Closed Open None of these

A: The given function: f:X→Y is continuous. That is, f(X)=Y is continuous. Then, E is the subset of Y…

Q: In which of the following intervals is f(x) = continuous? Vx-2 A (- 00, + 0) [2, + 0) (2, + 0) [1,2]…

A: f(x)=1x-2for continuous  function x-2 should not be negative because we will get imaginary value…

Q: Find all the saddle points of the function. f(x.y)=xsin O (5 m, 0) O (5 Tom, 1) 이름이 O (0,5 m) 1/5

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Q: The lower limit in the lowest class interval should be equal to i. a. False O b. True

A: Frequency distribution table : A frequency distribution table is one approach to organize data to…

Q: If f is continuous on [a, b], then the horizontal line y = k for every k between f (a) and f (b)…

A: If function 'f'  is continuous on closed interval [a, b], and if f(a)≠ f(b), then for any number k…

Q: For what value of b is

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Q: If f is continuous, then b+c f(x)dx = ] -S Fx - c)dx f(x – a+c

A: Translation along the horizontal axis can be obtained using the transformation rule x→x-a on the…

Q: In which graph is the functiorr continuous between x = O and x = =D5?

A: Consider the graphs of the function. Here, the objective is to identify the function which is…

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

A:

Q: Let A(x) f(t)dt, with f(x) shown in the graph below. -3- ** * T?

A: As per the fundamental theorem of calculus, given a function A(x)=∫0xf(t) dt, the derivative of this…

Q: Sßx² – 3 (Вх + 2 if (b) Suppose that f(x) if Find the value of ß so that f(x) is continuous…

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Q: x + 1, x 2 – 2x, |x² – 4x + 1, x > 2 x < 2 48. f(x)

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

A: The given function is gx=x,x&lt;-2bx2x≥-2. Assume that g is continuous function.

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

A: Given- fx=xx2-4 To find- The values of x at which the function is not continuous. Concept used-  The…

Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

A:

Q: O No, because f is not continuous on the closed interval [a, b].

A: Given that: The function f ( x) = x2 - 81x - 4     ,  [ -9, 9  ]  .

Q: 77. In Exercise 74, let S0.08x, p(x) = l0.06x + k, for x > 100. for x s 100, Find k such that the…

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Q: Let F(x)= ^4sqrt(x) A. Find the linearization of F(x) at x=16 B. Use your answer in part (a) to…

A:

Q: ) For what value of a is fx² -1 x<3 S(x)= { |2ax x23 Continuous at every x?

A:

Q: Let f(x) = ax* + bx . If (1,6) is a relative extremum point, then b is?

A:

Q: If X is continuous on the interval 0 to 10, t O True False

A: For a continuous distribution, and there exist infinite points.

Q: find the t-intervals on which c(t) = (t2, t3 − 4t) is concave up.

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: Find the value of c such that

A: Given∑n=0∞enc=7

Q: 86. If f is continuous and f (x) dx = 4, finc

A: Given that: ∫09f(x)dx=4

Q: x + 6|, if x - 1 x² – 3x

A:

Q: At what points of R² is the following function continuous? ху if (x.y) (0,0) f(x.y) = { 5x2 + 5y² if…

A:

Q: Use the formal definition to show that the function f(x) = x³ + 4x2 is not uniformly continous on…

A: Consider the given function. fx=x3+4x2 Given a small positive real number ε, uniform continuity…

Q: Q2/A) Decide if the following function is continuous using limits. flxl=2x,x«0 5Vx,x>0

A: We know that polynomials are continuous in their domain. Therefore, for x&lt;o, f(x)=2x and for…

Q: The function f(x) is continuous everywhere. FALSE O TRUE 3.

A:

Q: øz (@) is a continuous function of o in the range -o < @< ∞.

A:

Q: If ƒ(x) is continuous [-00,b]then on ſf(x)dx= lim [ ƒ (x)dx а. a a

A: Explanation of the solution is given below...

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: At what points of R² is the following function continuous? 17 f(x, y) = x5 (y² +81)

A: Solve the following

Q: Suppose f(x) is a bounded real - valued function on [a.b) such that fela,b] . Does it follows that…

A: A function is bounded in [a,b] if it can't achieve value beyond a and b. i.e.maximum acheivable…

Q: If f(2) = 13, f' is continuous, and | f'(t) dt = 27, f(6)? what is the value of Answer:

A:

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:

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.