Math, asked by Mel2019, 1 month ago

Ler be the 2x2 Identity matrix. Then which of the following is true for A?
1) A represents a rotation by 90 degrees
2) A represents a rotation by zero degrees
3) A represents a reflection under the line y=x
4) A represents a rotation by 180 degrees​

Answers

Answered by adityaverma0706
0

Answer:

EXPLANATION.

\sf \implies \lim_{x \to - 6 } \dfrac{\sqrt{(10 - x} - 4}{x + 6}.⟹lim

x→−6

x+6

(10−x

−4

.

As we know that,

Put the values of x = -6 in equation, we get.

\sf \implies \lim_{x \to - 6} \dfrac{\sqrt{10 - (-6)} - 4}{(- 6 + 6)}.⟹lim

x→−6

(−6+6)

10−(−6)

−4

.

\sf \implies \lim_{x \to - 6} \dfrac{4 - 4}{- 6 + 6}.⟹lim

x→−6

−6+6

4−4

.

\sf \implies \lim_{x \to - 6} \dfrac{0}{0}.⟹lim

x→−6

0

0

.

As we can see that it is in the form of 0/0.

We can simply factorizes the equation.

But if root is in 0/0 form we can simply rationalizes the equation, we get.

Rationalizes the equation, we get.

\sf \implies \lim_{x \to - 6} \dfrac{\sqrt{10 - x} - 4}{x + 6} \ X \ \dfrac{\sqrt{10 - x} + 4}{\sqrt{10 - x} + 4}.⟹lim

x→−6

x+6

10−x

−4

X

10−x

+4

10−x

+4

.

\sf \implies \lim_{x \to - 6} \dfrac{(\sqrt{10 - x})^{2} - (4)^{2} }{(x + 6) (\sqrt{10 - x} + 4)} .⟹lim

x→−6

(x+6)(

10−x

+4)

(

10−x

)

2

−(4)

2

.

\sf \implies \lim_{x \to - 6} \dfrac{(10 - x) - 16}{(x + 6) (\sqrt{10 - x } + 4)}.⟹lim

x→−6

(x+6)(

10−x

+4)

(10−x)−16

.

\sf \implies \lim_{x \to - 6} \dfrac{- x - 6}{(x + 6)(\sqrt{10 - x} + 4)}.⟹lim

x→−6

(x+6)(

10−x

+4)

−x−6

.

\sf \implies \lim_{x \to - 6} \dfrac{-(x + 6)}{(x + 6)(\sqrt{10 - x} + 4)}.⟹lim

x→−6

(x+6)(

10−x

+4)

−(x+6)

.

\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{10 - x } + 4)}.⟹lim

x→−6

(

10−x

+4)

−1

.

Put the value of x = -6 in equation, we get.

\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{10 - (- 6)} +4) }.⟹lim

x→−6

(

10−(−6)

+4)

−1

.

\sf \implies \lim_{x \to - 6} \dfrac{- 1}{(\sqrt{16} + 4)}.⟹lim

x→−6

(

16

+4)

−1

.

\sf \implies \lim_{x \to - 6} \dfrac{- 1}{8}.⟹lim

x→−6

8

−1

.

\sf \implies values \ of \ equation \lim_{x \to - 6} \dfrac{\sqrt{10 - x} - 4}{x + 6} = \dfrac{- 1}{8}.⟹values of equationlim

x→−6

x+6

10−x

−4

=

8

−1

.

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