arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B) arctan(ek*)In |cos(arctan(ek)- SIn sin(arctan(e**) CO d] +e C) arctan(ek)In sin(arctan(e**)- S In sin arctan(e**) dx +c ketx kekr 1+e2kx D) arctan(e**)In sin (arctan(e*))| + SIn |sin(arctan(e*) dx] +c ket* 1+e2kx E)(arctan(e*)In |stin(arctan(e*)| - S in |cos(arctan(e*) de] +e (arctan(e**))- kekx dx +c 2kx

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

A: Given: limx→∞xcos1x

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: sin(3ln(x) + 4)cos(3ln(x)+ 4)dx must be transformed into, The integration expression using suitable…

A:

Q: 25) Use Dr. Dai's Differential Table to find [tan - 1(x) ]' =, 25) A) 1/ (1+ x2) B) – tan-2(x) sec2x…

A:

Q: /1+cos x + V1- cos x X =-+÷,0<x<“ 4 2 V1+ cos x - V1-cos x - cOs X

A: Using trigonometry formulas we solve here given question

Q: Number 33

A: Given,

Q: * (D'+1)y(x) = tan(x) 1-sin(x) 1+sin(x) 1+cos(x) - y,(x) = sin(x)In m(x)s03 = (x) 2- -- y,(x) =…

A:

Q: 2x[ cos (3x) – 1] sin (6x) – 6x Use L'Hopital's Rule to evaluate lim 2x[cos (3x) – 1] lim sin (6x) –…

A:

Q: 0, 0 <x< A, f(x) ={1, n <x< 2x, sine series, period 6x 2, 2n <x < 3x;

A:

Q: 16. etan (1) sec² (x) dr

A:

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: y=-sec^-2 (In x)

A:

Q: cos²x 6. 1+ sin x = 1- sinx tanx - сotx 7. sec'x - csc?x = sin xcosx 8.1 tin cos2x = cscx - secx…

A: We have to verify that the given trigonometric identity.

Q: 2 n- tan x sec"- 9. Show that for n > 2, п-2 sec" x dx + n - sec" 1 x dx п — 1 | 4 Use this to find…

A: You need to use reduction formula to integrate the function, such that: You need to use integration…

Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: sin- In?| 4+ tan-!cos- dx 1+ cos2- 4+ tan-cos- 2sin- In2 4+ tan-'cos- dx 2 2 A 1+ cos 4+ tan-'cos- х…

A: Given integral ∫sin x2.ln24+tan-1cosx2dx1+cos2x24+tan-1cosx2

Q: lim sin(k/n). 1. cos(1) +5/3. 2. cos(1) +1/3. 3. cos(1) +2/3 4. cos(1) – 1/3.

A:

Q: Prove the identity. 1+ tanh(x) = e2x 1- tanh(x) 1 + cosh(x) 1+ tanh(x) 1- tanh(x) 1 cosh(x) cosh(x)…

A:

Q: 1-cos 2x lim x2 sec x-tan x lim X→0 X→- 2 x- 2 x2 +sin 3x lim 2x+tan 2x . х-0

A: We are solving first question for you. If you want solution for any other question than please…

Q: S(sec x tan x – 4x³)dx = - o tan x + х* + с sec x x4 + c sec x + x4 + c - sec x + x* + c - sec x x4…

A: Some of the properties of integration ∫f(x)+g(x)dx=∫f(x) dx+∫g(x) dx ∫xn dx=xn+1n+1+C ∫ (sec x tan…

Q: 4x[ cos (2x) – 1] sin (5x) – 5x Use L'Hopital's Rule to evaluate lim 4x[ cos (2x) – 1] lim sin (5x)…

A:

Q: integral Scos 4 (3x) Sin (3x) dx Evaluate the

A:

Q: sin x cos x – tan x cos² x dx cos x cos? x sin x dx cos3 x 16. = sec x dx + cos x Let u = cos x ; du…

A: It is given that    ∫cosx-tanxcos2x dx We have to evaluate it.

Q: First and second derrivative of: x Arctan x-In √x^2 +1=y

A: Given expression: x Arctan x-ln x2+1=y It can be written as follows: x tan-1 x-ln x2+112=yx tan-1…

Q: 8 sin x cos x sec x =

A:

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: S tan -) dx = a) x tan-1 (-) +÷In(x² + 1) + C b) x tan-1 () +글x2-글In(x2 + 1) + C c) x tan-1 (는) +글x2…

A:

Q: V1+ cos x + v1- cos x X =-+-,0<x<. 4 2 an 1+ cos x - V1- cos x - cOS X VI

A:

Q: 6. h(x) = 5x sin-1x 7. h(x) = tan x – tan-i x 8. h(x) = 3 sec-x 9. h(x) = 14 cot"x+ 12 cos-x 10.…

A: Since you have posted multiple questions we solve first question for you  To get the solution of…

Q: The first derivative of the function h is given by h' (x) = 3 ln(2 + cos(2x)) x, and the second -6…

A: Given: h'(x)=3 ln2+cos2x-xh''(x)=-6sin2x2+cos2x-1-2&lt;x&lt;2

Q: Non Homogeneous LDE yIII  -  yII  =  3  + sin x

A: Given differential equation is y'''−y''=3+sinx. We have to find the general solution of the given…

Q: cos*(x)dx

A: According to integration reduction formula ∫cosn(x) dx=n-1n∫cosn-2(x) dx+cosn-1(x) sin (x)n . For…

Q: sin 0 – cos 0 lim 0→x/4 tan0 – 1 2(cos x)2 + 3 cos x – 2 lim 2 cos x – 1 y In y – y lim y»e In(y5) –…

A:

Q: 6 x° cos(x) dx =. 6 x³ sin(x) + 18 x² cos(x) – 36 x sin(x) + 36 6 x³ sin(x) – 18 x² cos(x) – 36 x…

A: Integration by parts  ∫udv=uv-∫v.du

Q: 3) Find the expention of sin³ 0 4) Proof that: cosh iz = cos z 5) Prove that: cosh² z - sinh²z = 1…

A:

Q: cos4x - sin4x = cos 2 x 2 cos 2 x -cos 2 x

A:

Q: 2 *sinh“ x – sinh x+ cosh x dr -dx cosh¯ x

A:

Q: sin 2x + 2 arctan (k) lim x→0 In (1+ 3x + sin 2

A: Introduction: So, according to L'Hospital's Rule, if we have an indeterminate form 00 or ∞∞, all we…

Q: solve using L'Hopital's Rule 3.  Lim    (ex + e-x  - x2 - 2) / (sin2x - x2)    x->0

A: L'Hopital's Rule: The rule is applicable when the value of the limit function limx→af(x)g(x) is…

Q: 1. Lim 2×ー2xーメ+1 x-x3- 2x + 2 3. Lim メ→。 |- Cos X X-1 Sin 2x 2. Lim csc ax Csc 2x 4. Lim 7X 2x+5 x-…

A:

Q: lim x->-7  (-x-7)/(4-√(9-x)) lim x->-infinity (√6x^2 - 2x)/(x+8) lim x->0 (7x cos x + sin 5x)/3x

A:

Q: Integral of sin^4 (x/2) cos^2 (x/2 dx

A:

Q: limit as x approaches 0 of x^6*cos(4/x)

A:

Q: tanx – lim 0 Cos[1 – –

A: Given, -limx→0cos1-tanxx

Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

Q: 2x² + x + 3 x³ + x dx In[x] + In (x² + 1) + tan^³(x) + C Option 1 3 In]x] +In (x² + 1) + tan¹(x) + C…

A:

Q: 1-cos 2X lim x→0 x2 sec x-tan x lim X→- X- 2 x2+sin 3x lim r20 2x+tan 2x

A:

Q: acrsin x:! csc-1 x: arccos x: sec-1 arctan x: cot-lx: : [0, T] :: [0, 플] : (- 1 : (0, 27] :: [-플, 이…

A:

Q: Find delta value for the limit of x-->0 of tan5x/sinx when epsilon = 0.1

A: Introduction: The limit of a real-valued function is the base of differential calculus. A single…

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.