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Serggg [28]
3 years ago
7

Calculus 2

Mathematics
1 answer:
krek1111 [17]3 years ago
5 0

A simple way to see what was done is to add and subtract -1 from the numerator:

\dfrac{u^2-1+1}{u^2-1}=\dfrac{u^2-1}{u^2-1}+\dfrac1{u^2-1}=1+\dfrac1{u^2-1}

(provided that u^2-1\neq0, or u\neq\pm1)

###

Suppose you had a slightly more complex integrand, like

\dfrac{u^3}{u^2-1}=u+\dfrac u{u^2-1}

How do we know that? (Assume we don't already know the previous result, so that it's not just a matter of multiplying both sides by u.) Simple polynomial division:

u^3=\boxed{u}_{\,q}\cdot u^2, and u(u^2-1)=u^3-u. Subtracting this from u^3 gives a remainder of u^3-(u^3-u)=\boxed{u}_{\,r}, so

\dfrac{u^3}{u^2-1}=\boxed{u}_{\,q}+\dfrac{\boxed{u}_{\,r}}{u^2-1}

(where q and r denote "quotient" and "remainder")

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Answer:

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Answer:

1. Chloe has more money.

2. Dylan does <u>not</u> have enough money to buy 3 bags of candy.

3. Mikayla could get 4 pennies, 2 nickels, 2 dimes, and 2 quarters back in change.

Step-by-step explanation:

Penny = 1 cent

Nickel = 5 cents

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1. Chloe has 2 quarters(50 cents) and 3 dimes(30 cents). 50 + 30 = 80 cents

Haru has 5 nickels(25 cents) and 4 dimes(40 cents). 25 + 40 = 65 cents

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Answer:

77°, 103°

Step-by-step explanation:

x=103°

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-----------

∠5= 42°

∠3= 180°-42°=138°

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