Explanation Given information: The function f ( x ) = { x 2 − 9 x + 3 if x ≤ 4 k x + 5 if x > 4 . Explanation: Function is continuous at x = c when lim x → c − f ( x ) = lim x → c + f ( x ) = f ( c ) . First find the value of lefthand limit, lim x → 4 − f ( x ) . lim x → 4 − f ( x ) = lim x → 4 − x 2 − 9 x + 3 = lim x → 4 − ( x 2 − 9 ) lim x → 4 − ( x + 3 ) = ( 4 ) 2 − 9 4 + 3 = 16 − 9 7 = 7 7 = 1 Thus, lim x → 4 − f ( x ) = 1 . Now find the righthand limit lim x → 4 + f ( x ) . lim x → 4 + f ( x ) = lim x → 4 + ( k x + 5 ) = k ( 4 ) + 5 = 4 k + 5

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ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 14, Problem 7CT

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The value of k which makes the function continuous at c=4, where f(x)={x2−9x+3 if x≤4kx+5 if x>4.

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The value of k which makes the function continuous at c = 4 , where f ( x ) = { x 2 − 9 x + 3 if x ≤ 4 k x + 5 if x > 4 .

Solution Summary: The author explains the value of k which makes the function continuous at c=4, where f(x)=c

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The value of k which makes the function continuous at c=4, where f(x)={x2−9x+3 if x≤4kx+5 if x>4.

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Chapter 14 Solutions

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The value of k which makes the function continuous at c = 4 , where f ( x ) = { x 2 − 9 x + 3 if x ≤ 4 k x + 5 if x &gt; 4 .

Solution Summary: The author explains the value of k which makes the function continuous at c=4, where f(x)=c

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The value of k which makes the function continuous at c=4, where f(x)={x2−9x+3 if x≤4kx+5 if x>4.

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Chapter 14 Solutions

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The value of k which makes the function continuous at c = 4 , where f ( x ) = { x 2 − 9 x + 3 if x ≤ 4 k x + 5 if x > 4 .