Differential Approximation

lake_effect

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Apr 30, 2011
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The problem:

The range R of a projectile is

R = [(v^2)/32]*sin(2x)

where v is the initial velocity in feet per second and is the angle of elevation. If v = 2200 feet per second and x changed from 10° to 11°, use differentials to approximate the change in the range.

What I did:
stuck [(2200^2)/32]*sin(2x)into my ti-84, differentiated it at 10, and got the book answer (~4961ft).

However, when I differentiate it with pencil/paper, I get dR = [(2200^2)/32]*2*cos(2x)dx, and when I plug x=10 and dx=1 into that it gives ~284,257, clearly a lot higher than the book answer.

I can't figure out what's causing the inconsistency and it's giving me a headache. Anyone know what's up?
 
lake_effect said:
The problem:

The range R of a projectile is

R = [(v^2)/32]*sin(2x)

where v is the initial velocity in feet per second and is the angle of elevation. If v = 2200 feet per second and x changed from 10° to 11°, use differentials to approximate the change in the range.

What I did:
stuck [(2200^2)/32]*sin(2x)into my ti-84, differentiated it at 10, and got the book answer (~4961ft).

However, when I differentiate it with pencil/paper, I get dR = [(2200^2)/32]*2*cos(2x)dx, and when I plug x=10 and dx=1 into that it gives ~284,257, clearly a lot higher than the book answer.

I can't figure out what's causing the inconsistency and it's giving me a headache. Anyone know what's up?

dx = 1/180 * pi = 0.017453293 radian

Now you'll get the correct answer
 
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