sec2x-2taпх lim X→T/4 1+cos4x

Q: . lim, 1 -2 Inx x-1

A: To evaluate the given limit

Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

A:

Q: Q3 ex-(х+1) lim х>0 сosх-1 cosx-1

A: Use l hospitals  rule

Q: limx-->0 sin3x/ex-1

A:

Q: X x+cos (-3x) 16) lim

A: To find the limit  limx→-∞xcos-3x

Q: 1-cos x 9. lim x00 x2

A:

Q: V3x - 2 lim tan- %3D x + V3

A:

Q: tan x lim 3) Vx+1-1

A:

Q: 2Cos3xSenx +Sen2x Simplificar: E= %3D 2Cos7xCos3x- Cos10x

A: Given E=2cos3xsinx+sin2x2cos7xcos3x-cos10x To simplify this the identities used are…

Q: lim 0 3x²+5 cos x- 2x -5

A:

Q: Q4: A) solve: 1+xsin 1) lim- y0 1+xcos sin 2) lim -2m 20-4

A: Note: We are entitled to solve only one question at a time. To Find: i. limy→01+xsin1x1+xcos1xii.…

Q: -1 sin (5x) lim

A: The given expression is limx→0sin-15xx the given expression is the indeterminate form 00 Apply L'…

Q: 2x lim x→0 Vx + 1 – 1

A: Given limit expression is limx→02xx+1-1.

Q: dx Transforming using miscellaneous substitution will become secx +1

A: Our Aim is to transform ∫dxsec (x)+1-(i) using miscellaneous substitution.

Q: 6x-sin 2x 2x+3sin 4x 15. lim

A: Since you have asked multiple questions in single request. So we will answering only first question.

Q: æ In(sec(2æ)) (sin(3x))³ lim x→0

A: Given,             limx→0xlnsec2xsin3x3

Q: tan (2x) 3. 24. lim- %3D .3

A: We replace tan(2x) by sin(2x)cos(2x)…

Q: sin 3y lim y→0 4y

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

A:

Q: x5tan(x²) sec²(x²) dx

A:

Q: X – 1 limx → 1 V 4x – 2/x -

A:

Q: 2 2- limx-1 sin(x3-1) x-1

A:

Q: 1-coskx 2. lim = 0. kx

A: We have to find the limit of the function (1-coskx)/kx when x tends to 0 .

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: lim (- %3D x2 - 2sinx + 2x O 1 42

A:

Q: Vx+4 -2 1 limx¬0 ||

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: tan(1 – x) limx→1 2 2x +x – 3,

A: Limit

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: 2-y lim 7+ 6y² y-

A:

Q: ex+e¬x_x²-2 3. lim X--0 SIN²X-x2

A: The given limit  limx→0ex+e-x-x2-2sin2x-x2 This limit is in 0/0 form, so we can apply L' Hospital's…

Q: Find values of a and b such that sin 3x + ax + bx³ lim = 0 x3

A:

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: cos x-2sinx 1. limx-n 3cosx -2 limx-3 X-3 3x6-x*+2x-3 limy--o 4x5+2x3-5 iv. lim,→-1(x³ limy--1(x³ –…

A: [i]

Q: 1 1 dz = lim V3(w + h) – 2 V3w – 2 h 1- dw h-0

A:

Q: (1) lim,-0 √x+9-3 X (2) lim-0 1–c05x x sinx (3) limx-1 x²+3x-4 x-1

A:

Q: (2-4)² limx-1 sin(x3-1) x-1

A: by using limit algebra and L' hospital rule

Q: d) lim cos x sec (5x)

A: The given expression is :  limx→π-2cosx sex5x  Let,  x+h=π2  As x→π-2 so, h→0  cosx sec5x=cosπ2-h…

Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: 4 - V5t + 1 lim +3 vt +1– 2

A: Let L=limt→34-5t+1t+1-2

Q: 1. gx-) = - โ -เ sin 2x X< L2x

A: Given: gx-π=0x&lt;π12sin2xx≥π To find: Solution

Q: y= x°secx- 2xtanx y'-(x³)(secxtanx ) (9x*)(sccx)-( 2x)(sc x) + ( 2)(tanx) : 3x°. secx•3x² secxtanx•…

A:

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

A:

Q: 12) (Vy)* = sec-1 (x)

A: The detailed solution is as follows below:

Q: 2x (1) lim x→0 3– vx+ 9 -

A:

Q: y = (x – 1) 2x – x² + arcsin(x – 1) %3D - - - O - 12x – x² O - 2/2x – x² O V2x – x2 O 2v2x – x²

A: How to find the derivative of the given two functions.

Q: Find y': y = arc sec(x²) y = xVx - 1 2 y : xVI -x 2 y = xVx -1 x Vx - 1

A: Given: y=arcsec(x2)y'=dydx=ddx(arcsec(x2))We know that ddx(arcsec(u(x)))=11-1(u(x))2…

Q: 2+ sec (3x) (с) lim я (6 tan (3x) —1

A:

Q: Q1) Solve:- 5cosx cos" 1) lim * 4x-2n 2) lim х-2 х-2

A:

Q: steps: -x*-5x lim arctan 4+3x2-2. V1+4x6 b. lim lim (V9x2 + 2x + 3x) С.

A: Solving by limit theorem we have

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.