Question 1. The function f(x) is defined as follows: QUESTIONS (4x + 5x+7, f(x)=k, x a...

 

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Question 1. The function f(x) is defined as follows: QUESTIONS (4x² + 5x+7, f(x)=k, x <a x=a x> a x²-8x+37, NOTE: a and k are constants. Where appropriate, you should express your answers in terms of one or both of these constants. (a) Evaluate lim, f(x) or explain why it does not exist. (b) Evaluate lim f(x) or explain why it does not exist. (c) Find at least one (a, k) pair for which f(x) is a continuous function for x E R. (2+2+3=7 marks) Question 1. The function f(x) is defined as follows: QUESTIONS (4x² + 5x+7, f(x)=k, x <a x=a x> a x²-8x+37, NOTE: a and k are constants. Where appropriate, you should express your answers in terms of one or both of these constants. (a) Evaluate lim, f(x) or explain why it does not exist. (b) Evaluate lim f(x) or explain why it does not exist. (c) Find at least one (a, k) pair for which f(x) is a continuous function for x E R. (2+2+3=7 marks)

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