Consider the given limits (a is a constant, f(x) ≥ 0). lim_(x->a) f(x) = 0
lim_(x->a) g(x) = 0
lim_(x->a) h(x) = 1
lim_(x->a) p(x) = infinity
lim_(x->a) q(x) = infinity
Evaluate each limit below. If a limit is indeterminate, enter INDETERMINATE. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)

a.) lim_(x->a) [f(x)]^(g(x))

b.) lim_(x->a) [f(x)]^(p(x))

c.) lim_(x->a) [h(x)]^(p(x))

d.) lim_(x->a) [p(x)]^(f(x))

e.) lim_(x->a) [p(x)]^(q(x))

f.) lim_(x->a) (p(x))^(1\/(q(x)))

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

answer by yourhope:

hi! : )

a farmer that lived in ancient egypt would most likely be barried in the sand, in the desert!

: )