Expand everything in the limit:

We have
approaching 0, and in particular
, so we can cancel a factor in the numerator and denominator:

Alternatively, if you already know about derivatives, consider the function
, whose derivative is
.
Using the limit definition, we have

which is exactly the original limit with
. The derivative is
, so the value of the limit is, again, -14.
Answer:
72
Step-by-step explanation:
Find the LCM
6=2x3
8=2x2x2
9=3x3
12=2x2x3
LCM=2³x3²
=72
Answer:
(5, -3)
Step-by-step explanation:
Substitute -2x + 7 for y in the 2nd equation, and then solve the resulting equation for x:
-2x + 7 = 0.5x - 5.5
Combining like terms, 2.5x = 12.5, or x = 5.
Subbing 5 for x in the first equation, we get: y = -2(5) + 7 => y = -3
The solution is (5, -3)
Answer:
54yd
Step-by-step explanation:
Area for the rectangle=8×6
=48yrd
area for the triangle=1/2×4×3
=6yd
Total area=48+6=54yd
Answer:
4.1
Step-by-step explanation:
(4/5) * 20.5 = 16.4
20.5 - 16.4 = 4.1