Here are three equations. y = / a y = 3x + 3 y = 3x - 1 Draw a graph of each line. Use a table of values to help you. b Find the gradient and the y-intercept of each line. C All the equations are of the form y = 3x + c where e is an integer. Draw the graph of another line of.
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Answers
Answer:
⟹
x→a
lim
(
cot(x)−cot(α)
cos(x)−cos(α)
)
As we know that,
First we put the value of x = a in the equation and check their indeterminant form, we get.
\sf \implies \displaystyle \lim_{x \to a} \bigg( \dfrac{cos(\alpha ) - cos(\alpha )}{cot(\alpha ) - cot(\alpha )} \bigg) = \dfrac{0}{0} \ form⟹
x→a
lim
(
cot(α)−cot(α)
cos(α)−cos(α)
)=
0
0
form
It is 0/0 form indeterminant, we get.
Differentiate numerator and denominator of the equation, we get.
\sf \implies \displaystyle \lim_{x \to a} \bigg( \dfrac{- sin (x)}{- cosec^{2} (x)} \bigg)⟹
x→a
lim
(
−cosec
2
(x)
−sin(x)
)
\sf \implies \displaystyle \lim_{x \to a} sin^{3} (x)⟹
x→a
lim
sin
3
(x)
Put the value of x = a in the equation, we get.
⇒ sin³a.
\sf \implies \displaystyle \lim_{x \to a} \bigg( \dfrac{cos(x) - cos(\alpha )}{cot(x) - cot(\alpha )} \bigg) = sin^{3} a⟹
x→a
lim
(
cot(x)−cot(α)
cos(x)−cos(α)
)=sin
3
a
Option [A] is correct answer.