1. lim In (x –9) 2. lim log, (8x-x*) x3* x-2" 3. lim In (cos x) 4. lim In (sin x)

Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: For x = R, f(x) = log2 - sinx| and g(x)=f(f(x)), then (1) g'(0)=-cos(log2) (2) g is differentiable…

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Q: 8. lim

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Q: 6) lim (x – Ln(x² + 1)) X - X→∞

A: Here I am attaching image so that you understand each and every step.

Q: lim x → ∞ cos(16/x)^(13.32x^2)

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Q: lim sin4x / x x—>0

A: To evaluate the following limit. limx→0 sin4xx

Q: 1 Lim x+0 sin'x 2. X. X

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Q: S cos (z +1) z<-1 -1<z Let F (x) : e -1 Then lim F (1) =

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Q: an=(tan-1(n))/n, limn->infinity an=?

A: limn→∞ arctannnlimx→afxgx=limx→afxlimx→agx,   limx→agx≠0=limn→∞ arctannlimn→∞ n=π2∞ Apply…

Q: If y = f (x) = In (cosx), then, f' (x) =? O tan (x) O-sinx (x) -tan (x) O-cot (x)

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Q: cos(x) sin (2x) lim x X sin(x) – 1

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Q: Find the derivative of the following function. [In(2*)]* O 24|In(2*)]* 24|In (2*)]* 24|In(z")]* 24|…

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Q: Evaluate lim 4^(n)(1-cos(theta/2^(n))) as n approaches infinity.

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Q: lim x→0 (cos x)^(1/x^2)

A: we need to find the given limit

Q: The derivative of the function 3+ln x y = cos(ln x) is: cos(In x)+sin(In x)(3+1n x) ui cos(In…

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Q: lim cos(x) x- (7/2)* 1 - sin(x)

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Q: Question 2. Find lim sin (1 – 3e-/")e-/2. (Justify your solution.)

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Q: If f(x)=x3-x+2 find a formula for a. f'(x) b.f''(x) c.f'''(x) d. f(4)(x) (Experts how do I use…

A: given that, f(x)=x3-x+2

Q: Let f(x) = (In(x))ec(@), Find f'(x).

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Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: (2) limuy)-(0,0) In(1+x²y®) =,

A: When we put x=0 , y=0 in the function we donot get indeterminant form so we can put the values…

Q: 1-cos (xーT) lim X-n (x-)sin (x-n)

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Q: log(1+ x' Evaluate lim- x→0 sin° x 3.

A: Consider the limits,

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

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Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

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Q: Q3/ lim Evaluate 2 (1+ cosx) ) sec x

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Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

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