Factorize a^2–b^2 Hence find the exact value of 2557^2-2547^2

Mathematics

2 answers:

motikmotik2 years ago

8 0

Answer:

51,040.

Step-by-step explanation:

a^2–b^2 = (a - b)(a + b) so

2557^2-2547^2 = (2557-2547)2557+2547)

= 10 * 5104

= 51,040.

statuscvo [17]2 years ago

4 0

Answer:51040

Step-by-step explanation:a^2-b^2=(a+b)(a-b)

2557^2-2547^2

(2557-2547)(2557+2547)

(10)(5104)

51040

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Brilliant_brown [7]

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How to evaluate the limit

anzhelika [568]

$\displaystyle\lim_{x\to2}\frac{x^2-x+6}{x+2}$

Both the numerator and denominator are continuous at $x=2$ , which means the quotient rule for limits applies:

$\dfrac{\displaystyle\lim_{x\to2}(x^2-x+6)}{\displaystyle\lim_{x\to2}(x+2)}=\dfrac{2^2-2+6}{2+2}=\dfrac84=2$

Perhaps you meant to write that $x\to-2$ instead? In that case, you would have

$\displaystyle\lim_{x\to-2}\frac{x^2-x+6}{x+2}=\lim_{x\to-2}\frac{(x+2)(x-3)}{x+2}=\lim_{x\to-2}(x-3)=-2-3=-5$