Question 1: ( 10 Points)
Find all solutions to 2.0)12sin( −=−x for
[
]
π
π
,
−
∈
x.
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Calculus problems related to trigonometric functions, limits, derivatives, and inverse functions. It also provides solutions and methods to find the answers. Understanding these problems can be beneficial for students studying calculus in university or high school.
Typology: Exams
2012/2013
1 / 6
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Find all solutions to sin( 2 x − 1 )=− 0. 2 for x ∈[ −π ,π].
Find the derivative of 1
2 x + using the definition of the derivative (which involves a limit)
Find the following limits:
(a)
csc( 3 )
sec( 7 )
sin ( 2 )
tan( 7 ) lim 0 2 x
x
x
x
x →
(b)
x
x
x
sin( 3 ) lim → ∞
(c)
x
x
x
cos( 2 ) lim 0
→
Find the derivative of
(a) (^) ⎟
⎠
−
x
x
sec
1 2
(b) (^) ⎟
⎠
x
log (^3)
(c) arccos(sin x )
(d)
ln x 2
(e) y = f ( x ), where x
y 3 = , using (i) the definition of the logarithm
(ii) implicit differentiation
(f) ( )
1 f x
− at x = 2 , if f ( 1 )= 2 and f ′( 1 )= 3.