1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
anyanavicka [17]
3 years ago
7

Help. I need help with these questions ( see image). Please show workings.

Mathematics
1 answer:
Andrew [12]3 years ago
3 0

9514 1404 393

Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  \text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the <em>power rule</em>.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

You might be interested in
A = 100(1+r)^4<br> Expand the right of this formula.<br> appreciate your help with an explanation
suter [353]

Answer:

100r^4 + 400r^3 + 600r^2 + 400r + 100

Step-by-step explanation:

Expanding ( r + 1 )^4 gives :-

r^4 + 4r^3 + 6r^2 + 4r + 1

So multiplying 100 with r^4 + 4r^3 + 6r^2 + 4r + 1 gives :-

100r^4 + 400r^3 + 600r^2 + 400r + 100

4 0
3 years ago
Jayesh is looking into joining a gym. He has a budget of $65 per month. The gym he wants to join has fees based on the number of
puteri [66]
Number of visits can be only a whole number, the solution should be 9 visits
8 0
3 years ago
#3 is what I need help on
miv72 [106K]

Answer: 11.05

Step-by-step explanation:

Divide 5.20 by 8 to find the price of each bag (which is .65 cents.) Multiple .65 by 20 (13). 15% of 13 is 1.95. 13 - 1.95 is 11.05

PS: 1.95 is the discount. Hope this helps. Have a good day.

3 0
2 years ago
Read 2 more answers
Which inequality best represents the situation in which you must be at least 42 inches tall to ride the roller coaster
Romashka-Z-Leto [24]
42  \leq x

6 0
3 years ago
I don’t know how to do any of this
mojhsa [17]

Answer:

The length of x in #1 is 15.57

Step-by-step explanation:

Let's use #1 as an example to teach show you how to do this. In a right triangle we can solve these using trig. In this particular one, we have the measure adjacent to the angle and we are looking for the one opposite of the angle. So we look at all the trig functions and select the one that uses both of those two terms.

Sinα = Opp/Hyp

Tanα = Opp/Adj

Cosα = Adj/Hyp

As you can see, Tan is the function we are looking for. So we plug in all known information into that equation.

Tanα = Opp/Adj -----> Plug in known values

Tan(60) = x/9 ----->Calculate out the trig function

1.73 = x/9 -----> Multiply by the denominator to solve

15.57 = x

3 0
3 years ago
Other questions:
  • Find the value of the function sin 9pi/7?
    11·1 answer
  • Help pleaseeeee! It’s urgent
    13·1 answer
  • Is the square root of 96 rational or irrational
    12·1 answer
  • CAN SOMEONE HELP ME PLEASE!!!
    9·1 answer
  • she had a shoe box full of 5 cents 6 cents and 7 cents what totals could she make and what totals were impossible
    11·1 answer
  • Jose has a mask collection. He keeps some in a display case and the rest on the wall. 153 of his masks are on the wall, and 49%
    11·1 answer
  • Out of 100 employees at a company, 92 employees either work part time or work 5 days each week. There are 14 employees who work
    15·1 answer
  • Need hEli will give Brainly!
    5·1 answer
  • You invested $600 in a savings account that earns simple interest. After 20 years the account had earned $720 in interest. What
    9·1 answer
  • Math Is Hard For Me .
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!