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

Q: Prove that 1<x/sinx<π/2 for all x ∈ (0,π/2)

A: We are given: x∈0,π2 ⇒0&lt;x&lt;π2 Now, we know that sin x is increasing function in x∈0,π2…

Q: 1. f(t) = cos*t – sin*t 5. f(x) = tan 2x 1-cot 2x 2. y= sec20 – tan²0 3. f(x) = sin(cos x) %3D 3 4.…

A: Here we have to find derivative of given questions.

Q: f(x) 3 cos x 2 tan x - - f'(x) = f' 3 r()-

A:

Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Use the laws of logical equivalence to prove the equivalence below. A law must be stated as the…

A:

Q: prove that f(x) = sin*x + cos*x is a periodic function with periods

A: We use the Given Equations Prove that f(x) is a periodic function with period pie/2.

Q: Choose an equivalent statement for f'() if f(x)=² O-1 O sec(-)tan() n O-cot (1) n 1- cos x COS X…

A: Given,

Q: x+ cos X Find the derivative of tan x . O A) tan x+ tan xsin x+ xsec x+secx tan? x tan x(1+sin x) O…

A:

Q: Find the indicated maximum or minimum value of the objective function in the linear programming…

A: we have given a linear programming problem maximize f = 20x +50y x+2y≤48x+ y ≤302x+y≤ 50x≥0, y≥0 we…

Q: Dw many critical points does the fu

A:

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: Mean Value Theorem for the following function * f (x) cos x, x E [-π, π]

A: Given that  f(x)=cosx [-π,π]  To find the values of x that satisfy the mean value theorem

Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

A:

Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

A:

Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: HW/ Prove that: (1) 1-tanif x sechx

A:

Q: Let/(x)=sin³ x+A sin² X

A:

Q: 2) Consider the function f defined as: 3x f(x)=sin(x)' 2x + 3, a) Is f continuous at x ==? Explain.…

A: The given function,The aim is to find the following,(i) Check continuous at .(ii) Check…

Q: Let f be a function that is defined on the interval [-1,1] so that f(x) = image attachment.  Show…

A: Since given function is                   f(x)=x2sin1x+x2cos1x  ; x∈[-1,0)∪(0,1]     0;…

Q: Use a linear approximation to estimate the value of sin 0.06. Verify that f(x) = satisfies the…

A: Use formula of linear approximation

Q: Q\ Find all values of x that satisfy the 4 points Mean Value Theorem for the following function *…

A:

Q: Find the first derivative of sin x y = In 1+2 In x x cot x-2(In x) cot x-2 x(1+2 In x) x cotx+2(In…

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

Q: Compute the derivative d tan x dx \cos x COS X 4 sec2 x – sinx tan x 1– 4 cos x + tan? x - | (cos x…

A: We have to compute the derivative of the given function: ddxtan xcos x-4 We know the formula of…