Answer:
The answer is c
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
You differentiate top and bottom of the fraction until substitution gives you a value.
I can do the third one for you:
Lim x --> 0 of sin2x / sin3x
= lim x --> 0 of 2 cos2x / 3 cos 3x
= 2 cos 0 / 3 cos 0
= 2/3.
Limit as x--> 0 of (e^x - (1 - x) / x
= limit as x --> 0 of e^x + x - 1 / x
= lim (e^x + 1) / 1
= 1 + 1 / 1
= 2.
limit as x--> 00 of 3x^2 - 2x + 1/ (2x^2 + 3)
= limit as x --> 00 of 6x - 2 / 4x ( 00 = infinity)
Applying l'hopitals rule again:
limit is 6 / 4 = 3/2.
Limit as x --> 00 of (ln x)^3 / x
= limit 3 (Ln x)^2 ) / x
= limit of 6 ln x / x
= limit 6 / x
= 0.
We had to apply l'hopitals rule 3 times here,
Answer:
-3/4
Step-by-step explanation:
Get the coordinates of the two points and use the slope formula to find the slope.
We'll call the points point A and point B.
Point A's coordinates are (-3,1) and point B's coordinates are (1,-2)
Now, plug the numbers into the slope formula
Slope formula is: y2-y1/x2-x1
-2-1/1--3
-3/4
Answer:
The length of the edge of the cube = 4 inches
Step-by-step explanation:
* Lets describe the cube
- It has 6 faces all of them are squares
- It has 8 vertices
- It has 12 equal edges
∵ The volume of any formal solid = area of the base × height
∵ The base of the cube is a square
∴ Area base = L × L = L² ⇒ L is the length of the edge of it
∵ All edges are equal in length
∴ Its height = L
∴ The volume of the cube = L² × L = L³
* Now we have the volume and we want to find the
length of the edges
∵ Its volume = 64 inches³
∴ 64 = L³
* Take cube root to the both sides
∴ ∛64 = ∛(L³)
∴ L = 4 inches
* The length of the edge of the cube = 4 inches
Answer:
Option 2: (1, 0) and (0, -5)
Step-by-step explanation:
Let's solve this system of equations using the elimination method.
Start by labelling the two equations.
5x -y= 5 -----(1)
5x² -y= 5 -----(2)
(2) -(1):
5x² -y -(5x -y)= 5 -5
Expand:
5x² -y -5x +y= 0
5x² -5x= 0
Factorise:
5x(x -1)= 0
5x= 0 or x -1= 0
x= 0 or x= 1
Now that we have found the x values, we can substitute them into either equations to solve for y.
Substitute into (1):
5(0) -y= 5 or 5(1) -y= 5
0 -y= 5 or -y= 5 -5
y= -5 or -y= 0
y= 0
Thus, the solutions are (0, -5) and (1, 0).
