Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = x² + 7 - x, a= 4 b. 2t – 312 h(t) a = 1 1 + t3 C. f(x) = (x + 2r³)*, a = -1

Q: Consider the function if g(x) = if 2. if x>0. And study its continuity at x=0

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Q: f:R - R S6 – x2 x 2 1 x < 1 fx 4x + 1 x=1, x= -1-

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Q: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

Q: Let F(t)= (cost)i + (sin)j. (a) Show that + F = 0 (b) Show that there is no value of t on the range…

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Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Given the following piecewise function, demonstrate how to determine if f(x) is continuous on the…

A: determine if f(x) is continuous on the interval (-6, 6).

Q: Determine whether the following function is continuous at the given point x = 3x? + 14x – 5 1 x + 3…

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Q: Describe the interval(s) on which the function is continuous.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Find numbers a and b, so that f is continuous at every point.  f(x)= 20 , x-1

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Q: x² – 49 .2 if x + -7 f(x) : x +7 -12 if x = -7

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Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: Solve the following elimination. systems usiny Gauss- Jardan A. X-dy=8 3 x B. 5x +3y =9 -2x+y

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Q5. Explain why f(x) is not continuous at a. x2 - 25 f(x) = x + 5 if x #-5 a = - 5 if x =-5

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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.