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klio [65]
3 years ago
7

Please help me out!! :D

Mathematics
1 answer:
Rudik [331]3 years ago
7 0
T_n = a_1 + d(n - 1)


T_n = 52 + 12(n - 1)

T_n = 52 + 12n - 12

T_n = 40 + 12n

When n = 102,
T_{102} = 40 + 12(102) = 1264

Answer: 1264

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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 }

\mathbf{\implies  \lim_{x \to 0 } \ \  \dfrac{sec \ x - 1}{x}= c }

Provided that:

\mathbf{\implies  \lim_{x \to 0 } \ \  \dfrac{sec \ x - 1}{x}= \dfrac{0}{0} \ (form) }

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}

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\mathbf{\implies  \lim_{x \to 0 } \ \  \dfrac{sec \ x - 1}{x}=0 }

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6 0
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a path that is 7/8 of a mile long is divided into sections that are two sixteenth of a mile long how many sections are created?
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