Question

Calc, help! How do I determine at what points y=x+2/cos x is continuous?

Answer 1

where the function is defined

Answer 2

what's the def of continuous?

Answer 3

not at asymptote

Answer 4

its not defined in text so yeah im assuming

Answer 5

Definition in terms of limits of functions

The function f is continuous at some point c of its domain if the limit of f(x) as x approaches c through the domain of f exists and is equal to f(c).[2] In mathematical notation, this is written as

\[ \lim_{x \to c}{f(x)} = f(c).\]

In detail this means three conditions: first, f has to be defined at c. Second, the limit on the left hand side of that equation has to exist. Third, the value of this limit must equal f(c).

Answer 6

as x approaches what value is the function undefined

Answer 7

take the derivative

Answer 8

can you walk me through that step by step if possible? I missed the lecture and am somewhat lost

Answer 9

you need to use the quotient rule and the derivative of cos is -sin

Answer 10

f(x)/g(x)=l/m?

Answer 11

the function is not defined when \[x=\frac{ \pi }{ 2 }+k\pi\text{, where }k \in \mathbb{Z}\]

Answer 12

because cos x will be 0 at those values of x and the function will not be deifned there. thus, the function will be discontinuous at those points

Answer 13

so what you have above pi/2+ k(pi), how did you determine points off that?

Answer 14

y = x is continuous for all real x.

y = 2/x is continuous for all real x where x is not 0.

-1 <= cos x <= 1 for all real x.

thus, so long as cos x not = 0, your function will be continuous.

Answer 15

ohhhhh. Ok I got it now. Thank you!