Answer: 100+0+3
Step-by-step explanation:
A number that is not a whole number.
I think this is the graph for your answer, for the next question like this, try to use "Desmos"
The value of constant c for which the function k(x) is continuous is zero.
<h3>What is the limit of a function?</h3>
The limit of a function at a point k in its field is the value that the function approaches as its parameter approaches k.
To determine the value of constant c for which the function of k(x) is continuous, we take the limit of the parameter as follows:
![\mathbf{ \lim_{x \to 0^-} k(x) = \lim_{x \to 0^+} k(x) = 0 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%20%5Clim_%7Bx%20%5Cto%200%5E-%7D%20k%28x%29%20%3D%20%20%5Clim_%7Bx%20%5Cto%200%5E%2B%7D%20k%28x%29%20%3D%20%200%20%7D)
![\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}= c }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20%20%5Clim_%7Bx%20%5Cto%200%20%7D%20%5C%20%5C%20%20%5Cdfrac%7Bsec%20%5C%20x%20-%201%7D%7Bx%7D%3D%20c%20%7D)
Provided that:
![\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}= \dfrac{0}{0} \ (form) }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20%20%5Clim_%7Bx%20%5Cto%200%20%7D%20%5C%20%5C%20%20%5Cdfrac%7Bsec%20%5C%20x%20-%201%7D%7Bx%7D%3D%20%5Cdfrac%7B0%7D%7B0%7D%20%5C%20%28form%29%20%7D)
Using l'Hospital's rule:
![\mathbf{\implies \lim_{x \to 0} \ \ \dfrac{\dfrac{d}{dx}(sec \ x - 1)}{\dfrac{d}{dx}(x)}= \lim_{x \to 0} sec \ x \ tan \ x = 0}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5C%20%5C%20%20%5Cdfrac%7B%5Cdfrac%7Bd%7D%7Bdx%7D%28sec%20%5C%20x%20-%201%29%7D%7B%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%7D%3D%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%20%20sec%20%5C%20x%20%20%5C%20tan%20%5C%20x%20%3D%200%7D)
Therefore:
![\mathbf{\implies \lim_{x \to 0 } \ \ \dfrac{sec \ x - 1}{x}=0 }](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cimplies%20%20%5Clim_%7Bx%20%5Cto%200%20%7D%20%5C%20%5C%20%20%5Cdfrac%7Bsec%20%5C%20x%20-%201%7D%7Bx%7D%3D0%20%7D)
Hence; c = 0
Learn more about the limit of a function x here:
brainly.com/question/8131777
#SPJ1