8. Evaluate the following difference quotients and limits for the given functions: Function Difference Quotient Limits 2 a. g(x) g(x + h) – g(x) g(x + h)- g(x) lim h 0 x-3 h h b. t(x) = Vx t(x + h) - t(x) t(x +h)-t(x) lim h q(x + h) – q(x) q(x + h)- q(x) lim 3x c. q(x) = %3D 1-5x h
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![C. lim
8. Evaluate the following difference quotients and limits for the given functions:
Function
Difference Quotient
Limits
g(x + h) – g(x)
g(x + h)-g(x)
lim
2
a. g(x) =
x-3
b. t(x) = Vx
t(x + h) -t(x)
t(x +h)-t(x)
lim
%3D
q(x + h) – q(x)
q(x + h) - q(x)
lim
3x
c. q(x) =
1-5x
h
d. m(x) = x* - x³ + x?
m(x + h) - m(x)
m(x+h)-m(x)
lim
n(x + h) - n(x)
n(x +h) - n(x)
lim
e. n(x):
x2
r(x + h) – r(x)
r(x +h) - r(x)
8. r(x) =
lim
h-0
%3D
9. If an object is dropped from a high cliff, then the distance (in feet) traveled after t seconds is
given by the function d (t) = 16t2.
%3D
a. Find the difference quotient (average speed) over the interval [a, a + h]. Include units with
your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffccae16d-a3f5-4ed1-bb18-084e96e3fc22%2Fcf3e5df2-8730-481e-bedc-d729dc2ea779%2Fwwk6ien_processed.jpeg&w=3840&q=75)
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