Use the definition of continuity and the properties of limits to show that the f

shadsiei

shadsiei

Answered question

2021-10-17

Use the definition of continuity and the properties of limits to show that the function is continuous of the given number a.
f(x)=x2+7x,a=4

Answer & Explanation

pierretteA

pierretteA

Skilled2021-10-18Added 102 answers

Given function is :
f(x)=x2+7x To check the continuity at a=4
Calculate the left-hand limit,
f(a)=limh0f(ah)
=limh0f(4h)
=limh0[(4h)2+7(4h)]
=(16+3)
Right-hand limit at a=4
f(a+)=limh0f(a+h)
=limh0f(4+h)
=limh0[(4h)2+7(4h)]
=(16+3)
Calculate the value of f(x) at a=4
f(a)=f(4)
=42+74
=16+3
Left hand limit = right hand limit = f(a)
Thus, the given function is continuous at a=4
Jeffrey Jordon

Jeffrey Jordon

Expert2022-06-24Added 2605 answers

Answer is given below (on video)

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