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i'm having some trouble with evaluating limits if anyone could help me out a bit i would appreciate it. thanks in advance

evaluate the following limits:

Question 1:

lim

x -> 0 [tex]\frac{2tan^{2}x}{x^{2}}[/tex]

my answer:

u = x[tex]^{2}[/tex]

as x -> 0 u-> 0

= lim

u->0 [tex]\frac{2sin u}{u cos u}[/tex]

= 2 lim

u -> 0 [tex]\frac{sin u}{u}[/tex] (lim u-> 0) [tex]\frac{1}{cos u}[/tex]

= 2 (1) [tex]\frac{1}{cos (0)}}[/tex]

= 2 (1)(1/1)

= 2

question 2:

lim

x->0 [tex]\frac{1- cosx}{x sinx }[/tex]

my answer:

lim

x ->0 [tex]\frac{sinx}{x}[/tex] (lim x-> 0 [tex]\frac{1}{1 + cosx}[/tex]

(1)(1/2)

= 1/2

question 3:

lim

x -> 0 [tex]\frac{sin 7x}{sin 4x}[/tex]

my answer:

[tex]\frac{7sin 7x}{4 sin 4x}[/tex]

i'm not sure where to go from here on this one...i know the resulting limit will be equal to 7/4 but i dont know how to come up with this answer...i'm getting really confused

question 4:

lim

x->0 [tex]\frac{sin(cosx)}{sec x}[/tex]

= [tex]\frac{sin(cosx)}{1/cosx}[/tex]

= sin(cos) x . (cos x)

= sin(cosx[tex]^{2}[/tex])

= sin(cos (0)[tex]^{2}[/tex])

= 0.84

I am really unsure of what i am doing here...i know its a lot to look at, i really appreciate the help. Thank you!