156 is even or odd number

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

2 years ago

If DGH ~ DEF, Find the value of X

DIA [1.3K]

Answer:

$x=25$

Step-by-step explanation:

we know that

DGH ~ DEF ---> given problem

Remember that

If two triangles are similar, then the rtio of its corresponding sides is proportional and its corresponding angles are congruent

so

$\frac{DG}{DE}=\frac{GH}{EF}$

substitute the given values

$\frac{52}{91}=\frac{x+3}{2x-1}$

$(2x-1)52=(x+3)91\\104x-52=91x+273\\104x-91x=273+52\\13x=325\\x=25$

4 0

3 years ago

Click on a factor pair of 32.

jasenka [17]

Answer:

1, 2, 4, 8, 16, 32

Step-by-step explanation:

Mark me Brainllest

8 0

2 years ago

4. Tikili wants to invest $3500 at her local bank. She will receive an interest rate of 5% compounded

alexandr402 [8]

Answer:

$3863.35 = 3500(1 + \frac{0.05}{2} )^{(2 \times 2)}$

Step-by-step explanation:

The formula for this equation is

$a = p(1 + \frac{r}{n} )^{(n \times t)}$

a is the final result

p is the starting amount (deposited)

r is the interest rate

n is the number of times it's compounded

t is the time

because it says compound annually and it's after 2 years both t and n equal 2. I rounded a for you, but if you don't need it rounded here it is: 3863.345117

Please double check me I may be wrong, this is my second time doing these type of questions

3 0

3 years ago

PLEASE I AM IN DESPERATE NEED OF HELP

erastova [34]

Answer:

C: H > 60

Step-by-step explanation:

H is 60 in or taller, underlined indicates that it's also 60 in, not just above it.

8 0

2 years ago