1 A function g is defined by x<1 g(x)={x+1, (x-4)° +5, x24 18x<4 Sketch the graph of y = g(x). (a) Find lim g(x), lim g(x) and g(1). Is g(x) continuous at x= 1? (h) Find lim g(x), lim g(x) and g(4). Is g(x) continuous at x = 4?

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Q: Q 4) (1) If lim f (æ) = 18 and +3 lim g (1) = 29 then find lim [3 f (x) + 5 g (x)]

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Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

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A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

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Q: b) Let f(x) = x²-1 2-1 ' √x-1 0 < x < 1 1<x<3 2-1 ' 5x+3, 3x Find lim, 1 f(x). 3x-7 c) Let f(x) =…

A: The b part of the question can be solved using the concept of limits.The c part of the question can…

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