## Calculus (3rd Edition)

The tangent line at $x=0$ is given by $$y=1.$$
Since $y=x^3+\cos x$, then the slope at $x=0$ is given as follows $$y'=3x^2-\sin x\Longrightarrow m=y'(0)=0.$$ The equation of the tangent line at $x=0$ is given by $$y=(0)x+c=c.$$ To find $c$ we use the fact that the tangent line and the curve coincide at $x=0$, so we have $y(0)=1=c$. Hence the equaion of the tangent line at $x=0$ is given by $$y=1.$$
The passage describes the process of finding the equation of the tangent line to the curve \( y = x^3 + \cos x \) at \( x = 0 \). It includes the calculation of the slope and the y-intercept.
no_question

the text does not contain a mathematical question; it is a detailed explanation of a mathematical process.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Calculus (3rd Edition)

The tangent line at $x=0$ is given by $$y=1.$$
Since $y=x^3+\cos x$, then the slope at $x=0$ is given as follows $$y'=3x^2-\sin x\Longrightarrow m=y'(0)=0.$$ The equation of the tangent line at $x=0$ is given by $$y=(0)x+c=c.$$ To find $c$ we use the fact that the tangent line and the curve coincide at $x=0$, so we have $y(0)=1=c$. Hence the equaion of the tangent line at $x=0$ is given by $$y=1.$$
user
The passage describes the process of finding the equation of the tangent line to the curve \( y = x^3 + \cos x \) at \( x = 0 \). It includes the calculation of the slope and the y-intercept.

TYPE: NO_QUESTION

The text does not contain a mathematical question; it is a detailed explanation of a mathematical process.