ENGG MATH 2 1. lim- X--0 x2 1-cosx 2 sec?x-2tanx 2. lim X-n/4 1+cos4x Vx² +3 3. lim X-00 x 4. lim X-0 In(1+x) Arctanx 5. lim - 1 X0 xsinx x2 6. lim Ty-1 y-0 2y2 'y(e2ny-1) sin2x(1-cos2x) 7. lim X-0 (Arcsinx)-sinx xsinx 8. lim- x-0 ex+e-x-2cosx 9. lim(1 + sin?x) X-0

Q: Find g'(x) if g (x) = 5√x tan x. 5(2 cot x+tan x) 2√x 5 tan x(2x sec x+1) 2√x 5(x sec² x+2 tan x)…

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Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: lim f(x) as x --> 0 for (5 + 2x + sinx)/(6cosx). I did substitution but I don't understand why…

A: We have given,

Q: х-tanx 2. lim х30 1-со 3 3. lim sinx lnx = 0 x→0+

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Q: X – sinx (i) lim x2 d (ii) ( e2x · cos x) dx (iii) J tan 2x dx d (iv) dx ( sech 2x) 1 (v) -) dx S(…

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Q: S(sec a tan x 5æ4)dx tan x + x +c - sec x + x' + c sec x – x5 + c sec x + x +c sec x – x + c

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Q: 2x-1 Let f (x) = %3D x+2 Find f' (x). First set up the limits and simplify Using equation (6) from…

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Q: Q2/ Find f (x) : 1- f(x) = 4 cos x + 2 sin x 2- f(x) = cos x - x csc x 3- f(x) %3D %3D cot x 1+cscx…

A: As per guidelines we can solve only one question at a time. So the first question can be solved as…

Q: How would you denote ƒ' (−1) if ƒ(x) = x² + 3x +2? f(x)-f(-1) x+1 limħ-1 limä→-1 limh→0 limh→0…

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Q: why is limx->0[x^4 * cos(2/3x)] not equal to zero? I thought that if I plug in zero to x^4 it makes…

A: Given that: limx→0x4.cos23x

Q: 1 sinx # 1-cos2x ẩu! (6 2

A: Given query is to find the value of the limit.

Q: 9) Use lim (a) lim sinx sin6x x+0 sin4x = 1 Find the limits. (b) lim 1-cos²x X-0 X

A: Answer (a)limx→0​sin4xsin6x​Multiplying and dividing the numerator by 6x and denominator by…

Q: sin6x V1. Tentukan hasil dari limit berikut lim- x-0 5x Jawab: . sin4x + sin2x V2. Tentukan hasil…

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Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: find Vx+4--x-2 1- lim --3 x+3

A: Since we are given with the multiple number of question and our guideline is solve first question…

Q: sinx lim x-0 x-xcos x

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Q: * /Q3 e*-(x+1) lim X→0 CoSx-1 %3D -1 1 -2 O O O O

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Q: lim t →0  (e^6t i + (sin(7t)/ (7t)) j + e^−4t k)

A: Limit :

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: 2x-arcsinx 7. lim x→0 2x+arctgx emx. 8. lim х-0 пх In(1+3*) 9. lim x→-o In(1+2*)

A: There are multiple question so as per Bartleby policy  I have answered two question, Kindly ask…

Q: 419 *Ocosec™* 6d8 is equal to

A: Given integral is ∫sec4/9θ cosec14/9θ dθ

Q: S sec° (x) dx Select one: sec“(x) cot(x) O see't) col62) + ¿( sec(x) tan(x) + ¿In|tan(x) + sec(x)|)…

A: We will use bi parts to solve these type of integral.

Q: 35. lim (sec 2/2 x – tan æ)

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Q: Arcsinx-sinx 1. lim y→0 (1-cos2x)sin2x

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find the discontinuities, if any.  f(x) = sin (x^2 - 2)  f(x) = sec x lim    sin θ / θ2 θ→0+

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Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

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Q: Suppose fx) -2x2-3x. To compute f'(x), which Limit should be evaluated?

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.