i'm trying to figure out the problem the limit of sin x over x + tan x as x approaches 0
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Get your answer in degrees. Divide it by 180 then multiply with pi.
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<--- also not sure why you asked about sin(1).
Alternatively, and more expectedly if you are submitting this as HW to your teacher (I doubt your teacher suspects students will be able to relate limits of sin(x) / x and tan (x) / x and believe it is your work), they want you to use L'Hopital's rule:
sin x / (x + tan x) = 0 / 0 as x -> 0
apply L'Hopital's rule
cos x / (1 + sec^2 x ) = 1 / (1 + 1) = 1/2 as x -> 0, note sec x = 1 / cos x
Alternatively, and more expectedly if you are submitting this as HW to your teacher (I doubt your teacher suspects students will be able to relate limits of sin(x) / x and tan (x) / x and believe it is your work), they want you to use L'Hopital's rule:
sin x / (x + tan x) = 0 / 0 as x -> 0
apply L'Hopital's rule
cos x / (1 + sec^2 x ) = 1 / (1 + 1) = 1/2 as x -> 0, note sec x = 1 / cos x
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lim((sinx/(x+tanx)) as x goes to 0
=lim ((sinx/x)/(1+tanx/x))
But sinx/x and tanx/x both go to 1 as x goes to zero
So the limit is
1/(1+1)=1/2
not sure why you asked the question about sin(1)
=lim ((sinx/x)/(1+tanx/x))
But sinx/x and tanx/x both go to 1 as x goes to zero
So the limit is
1/(1+1)=1/2
not sure why you asked the question about sin(1)
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sin (1) = sin (pi/180) because pi radians = 180 degrees..............Ans