Y = xe^x
dy/dx(e^x x)=>use the product rule, d/dx(u v) = v*(du)/(dx)+u*(dv)/(dx), where u = e^x and v = x:
= e^x (d/dx(x))+x (d/dx(e^x))
y' = e^x x+ e^x
y'(0) = 1 => slope of the tangent
slope of the normal = -1
y - 0 = -1(x - 0)
y = -x => normal at origin
Correct option B)
.
<u>Step-by-step explanation:</u>
We have the following figure attached as shown below.
Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:
2 similar right angled surfaces
We know that area of triangle = 
⇒ 
⇒ 
⇒ 
But there 2 such surfaces so , 
3 rectangular surfaces
Area of rectangle = 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
Total area =
Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:
=
Correct option B) .
Looks like the integral is supposed to read
The same integral in the required order is
In 3 hours, the two planes will be 2,700 miles apart.
If in one hour, the planes get 900 miles apart, it will take 3 hours to become 2,700 miles apart.
《----- and -----》 Indicatethe planes moving in opposite directions.
The number indicate the distance traveled.
The amount of times the number is repeated indicates the amount of hours flown (ex.: 50+50+50+50 would indicate 4 hours flown because there are 4 50s in the sequence).
So
《-----300 + 600-----》
=900 miles in one hour
《------300+300 and 600+600-----》
=1,800 miles in 2 hours
《-----300+300+300 and 600+600+600-----》
=2,700 miles in 3 hours
