A. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
g(x) = x3 cot(x) + 6x cos(x)
B. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
f(x) =
x2 + x − 7
x2 − 7
C. Use the Product Rule or the Quotient Rule to find the
derivative of the function.
f(x) = (8x2 + 4)(x2 − 6x − 9)
A.) State Product Rule, Quotient Rule, and
Chain Rule.
B.) Prove Power Rule
C.) Prove Product rule:
-By definition of derivative
-By implicit differentiation
D.) Prove the Quotient Rule
-By definition of derivative
-By implicit differentiation
-By product rule and chain rule
7. Use the Product Rule and the Sum Rule to determine each of
the following probabilities:
Mendel mated Yellow Round peas (YYRR) to Green Wrinkled peas
(yyrr), then performed an F1 selfcross (YyRr x YrRr). What is the
probability that an F2 pea chosen at random is heterozygous for
both genes?
From the YrRr x YyRr self cross: What is the probability that
an F2 pea chosen at random is heterozygous for the Y gene OR the R
gene?
Cystic...
Section 3.3 Product and Quotient Rules and Higher-Order
Derivatives
Find the derivative of the function
g(s)=√s(s^2+8)
g(x)=√x sinx
f(x)=x^2/(2√x+1)
f(t)=cost/t^3
y=secx/x
f(x)=sinx cosx
y=(2e^x)/(x^2+1)
Find equation of the tangent line to the graph of the function
f(x)=(x+3)/(x-3) at the point (4, 7)
Find the equation of the tangent line to the graph of the function
??=24?3 at the point (1, 2).
write the appropriate equilibrium reaction for each problem. Use
the quadratic equation if the 5% rule does not apply. Show all
work.
1. Calculate the Ka of a .48 M weak acid HA if the pH of the
solution is 3.45
2. A weak base has a Kb of 1.050E-03. Calculate the pH of a .225
M solution of the weak base.
Evaluate whether each of the following statements are true or
false.
It is appropriate to compute the correlation coefficient when
one of the variables is ordinal as long as at least one variable is
in interval. (True/False)
R (correlation coefficient) between X and Y represents the
percentage of variability of variable X explained by variability of
variable Y (True/False)
When correlation coefficient is negative, standard error of
prediction is also negative (True/False)
When correlation coefficient is positive, beta (B) value...
Use the Chain Rule to find the indicated partial derivatives. N
= p + q p + r , p = u + vw, q = v + uw, r = w + uv; ∂N ∂u , ∂N ∂v ,
∂N ∂w when u = 4, v = 2, w = 8
For each of the following sets of results, compute the
appropriate test statistic, test the indicated alternative
hypothesis, and compute the effects size(s) indicating their
magnitude:
set
hypothesis
1
2
D
n
α
a)
μ1 ≠ μ2
32.6
32.1
4.2
24
0.05
b)
μ1 > μ2
101.9
95
10
27
0.01
c)
μ1 < μ2
74.6
70.2
6.6
24
0.10
a)
Compute the appropriate test statistic(s) to make a decision about
H0.
critical value? = ; test statistic? =
Decision?: ---Select--- Reject...
For each of the following sets of results, compute the
appropriate test statistic, test the indicated alternative
hypothesis, and compute the effects size(s) indicating their
magnitude:
set
Hypothesis
μ0
σ
n
α
a)
μ ≠ μ0
51.4
50
3.6
49
0.05
b)
μ > μ0
39.7
40.1
6.2
31
0.15
c)
μ < μ0
31.8
30
8.9
33
0.10
a)
Compute the appropriate test statistic(s) to make a decision about
H0.
critical value =__________ ; test statistic =
________________
Decision: ***(choose...