2. Show that by using MEAN VALUE THEOREM 4-n < tan-1 v – tan-1 u < 1+v2 if 0< u

Q: cosh 1+j T 2 * T sin 1-j- 2

A:

Q: 4) Consider the function defined by 10) = /3 (sin (5 + *)) (증+0)) +4 V3 sin (+t) + 4+ V/3 (cos G…

A: we have to show that f(t) is a constant

Q: (a) [(0.6e15 + 4t 3t² +03-10-01 at 4t4-3t3 + 0.3 _10t 1.5 -0.1 2t3 (b) Evaluate…

A:

Q: 154. We can obtain a useful linear approximation of the function f(x) - 1/(1 + tan x) at x- O by…

A: The given function is fx=11+tanx

Q: *The interval [a, b] for a function x^3 - 4 x- - ...... 9 = 0 is [2,3] O [0, 2] O [0, 1] O [1, 2] O

A: We need to find the interval for a function f(x)=x3-4x-9=0

Q: * /Q18 When x = acsc 0, ÷tan 0 = a

A:

Q: (a) The averages of cos x and lcos x| from 0 to x are (b) The average of the numbers v,, the average…

A:

Q: The limit of n tan(-) as n-∞is equal to 1

A:

Q: 2. Height travel by the rocket in first 6 seconds is given by s = (5 103) || In (T00-4) dt- 180…

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

Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

A:

Q: The maximum value of y = cos x for - < x< is 1

A:

Q: State the Mean Value Theorem. Use it to show that for all x ≥ 0, 0 ≤ tan^−1 x ≤ x. [Hint: Use Dx…

A:

Q: 16) Prove the 1+ tan?(u) = sec2(u).

A:

Q: by using mean value theorem prove |sin(x) – sin(y)I < ]x – y|

A: To prove sinx-siny≤x-y Let f(t)=sint ∀t∈(x,y) Then we have the mean value theorem f'(c)=f(x)-f(y)x-y…

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

A:

Q: Using the relation z=x+iy = rcosθ + irsinθ=re^iθ . Derive z^n = r^n(cosθ + isinθ)^n = r^n(cosnθ +…

A:

Q: V sing the Successive Appoximation Method. Find the root OF Finction 1+cosx X= Gorrect: your ans…

A: AS PER BARTLEBY GUIDELINES, ONLY FIRST QUESTION IS TO BE SOLVED.     Given that, x=1+cosx3 We need…

Q: The sum of the absolute max and the absolute min of the function f(x) = = sin 2x + cos is equal to:

A:

Q: Compute * sin x dx. x4 + 1 p.v.

A:

Q: Prove that • tan'z = —— In ( + + ²/² ) 1-Z

A:

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Prove that 1+ cos x + V1-cos x X +,0<x<" 4 tan %3D 1+ cos x -V1- cos x 2

A:

Q: f(x) = 2 tan(cos x)

A:

Q: Find all values of sin-V2 Given Z, = -1 + iv3 and Z, = -v3+i, show that In (Z,.Z2) # lnz, + InZ2 %3D

A: (a) We have to find all values of sin-12

Q: (a) (c) Evaluate Stan³xsec³ xdx X 5 sec²³x+C tan x- tan x+C (b) (d) X -sec*x+C tan x-- x-t 4 tan¹…

A:

Q: = Use The Intermediate Value Theorem to prove that there is at least one solution to tan(0) = (0 -…

A: