[tex]\bold{ \lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1} } = \bold{-\frac{\sqrt{2} }{8} }[/tex] , the correct answer is option (C)
What is limit?
"A limit is the value that a function approaches as the input approaches some value."
What is substitution in mathematics?
"Substitution is the process of replacing an algebraic letter with its value. "
Given: [tex]\lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1}[/tex]
By substitution the value of limit,
[tex]\lim_{x \to 3} \frac{cos(\frac{\pi x}{4} )}{x+1}[/tex]
= [tex]\frac{cos(\frac{\pi (3)}{4} )}{(3)+1}[/tex]
= [tex]\frac{cos(\frac{3\pi}{4} )}{4}[/tex]
= [tex]\frac{-\frac{1}{\sqrt{2} } }{4}[/tex]
= [tex]-\frac{1}{4\sqrt{2} }[/tex]
= [tex]\bold{-\frac{\sqrt{2}}{8} }[/tex]
Hence, option (C) is the correct answer.
Learn more about limit here:
brainly.com/question/1619243
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