Calculus Examples

$lim_{x \to 1} (\sin (x)) + \cos (x)$

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $1$ .

$lim_{x \to 1} \sin (x) + lim_{x \to 1} \cos (x)$

Move the limit inside the trig function because sine is continuous.

$\sin (lim_{x \to 1} x) + lim_{x \to 1} \cos (x)$

Move the limit inside the trig function because cosine is continuous.

$\sin (lim_{x \to 1} x) + \cos (lim_{x \to 1} x)$

Evaluate the limits by plugging in $1$ for all occurrences of $x$ .

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Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\sin (1) + \cos (lim_{x \to 1} x)$

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

$\sin (1) + \cos (1)$

Simplify the answer.

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Simplify each term.

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Evaluate $\sin (1)$ .

$0.0174524 + \cos (1)$

Evaluate $\cos (1)$ .

$0.0174524 + 0.99984769$

Add $0.0174524$ and $0.99984769$ .

$1.0173001$