For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality − 1 ≤ 6 − x 5 ≤ 7
For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality − 1 ≤ 6 − x 5 ≤ 7
a. Identify the type of equation or inequality (some may fit more than one category).
b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.
• Linear equation or inequality
• Quadratic equation
• Rational equation
• Absolute value equation or inequality
• Radical equation
• Equation in quadratic form
• Polynomial equation
degree
>
2
• Compound inequality
−
1
≤
6
−
x
5
≤
7
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
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