f(x) = (x + 2x^3)^4 a= -1 g(t) = t^2 + 5t/2t + 1, a = 2 p(v) = 2 Squareroot 3 up

Question

f(x) = (x + 2x^3)^4 a= -1 g(t) = t^2 + 5t/2t + 1, a = 2 p(v) = 2 Squareroot 3 upsilon^2 + 1, a = 1 f(x) = 3x^4 - 5x +^3 Squareroot xx^2 + 4, a = 2 Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. f(x) = .v + Squareroot x - 4. [4. infinity) Explain why the function is discontinuous at the given number a. Sketch the graph of the function. f(x) = 1/x + 2 a = -2 f(x) = {1/x + 2 if x notequalto -2 1 if x = -2 a = -2 f(x) = {x + 3 if x lessthanorequalto -1 2^x if > -1 a = -1

Explanation / Answer

16. g(x)= (x-1)/(3x+6) , (-infinity,-2)

A function is continuous at a number a if limit at x tends to a of f(x) = f(a)

so lets take a point in this interval .Lets take a=-3

lim x tends to -3 ((x-1)/(3x+6)) =(-4)/(-3)=4/3 which is equal to f(-3)

Hence the given function is continuous in the given interval.

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