Prove that 1

Q: Prove that the inequality sinx+tanx>2x holds in the interval (0,π/2).

A:

Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: Q2. Prove that sec2(tan-x) = 1+ x?

A:

Q: The largest value of the non-negative integer a for which lim x →1 - ax + sin(x - 1) + a x + sin(x −…

A:

Q: Prove that V1+ cos x +VI-cos x X +÷,0<x<. 4 TT - 1+ cos x -V1- cos x 2 2

A: PS: There seems to be a cut in the image. If this is the question, pls find below its solution.

Q: Evaluate the definite integral 3 2 sin (z)dr using Part 1 of the Fundamental Theorem of Calculus. 4…

A:

Q: 7. Prove that cos(sin¬'r) = V1- x². 8. Evaluate f dr

A: follow next step

Q: Show that |cos x - 1| &lt;=|x| for all x-values. (Hint: Consider ƒ(t) = cos t on [0, x4].)

A: Mean value theorem states that

Q: tan(2 – j5) j(2-j5) +7- jv2 In(-5)| (3220° – sin 20 + jln5)*|

A:

Q: a) Show that: tan z, + tan z, tan(z, + 2) = 1- (tan z) +(tan z)

A: To prove the formula:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: (b)Prove that if f (x) = In (cosx), then f'(x) = -tanx.

A:

Q: 4. Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x³ - 9x on the…

A:

Q: 4. Prove the identity: sin x + tan x = tan x cos x + 1 (sinx¥, sin x COS X LS = cosx + 1 V sin x cos…

A:

Q: Evaluate the definite integral 3 2 sin (2)dx using Part 1 of the Fundamental Theorem of Calculus. 57…

A:

Q: V/ Prove that: (1) tanx= cot

A:

Q: Prove that for all whole numbers n ≥ 1,

A: Explanation: Given that,  n≥1dndxnsinx=sinx+nπ2   Formula Used: 1. ddxsinx=cosx 2. ddxcosx=-sinx

Q: tan °(ln z) sec® (In z) Evaluate dz.

A: Evaluate: ∫tan3lnxsec6lnxxdx

Q: Is it true that tan (tan-x) = x for all x? Is it true that tan-(tan x) = x for all x?

A: Given statements are tantan-1x = x  for all x. tan-1tan x = x  for all x. We have to check if these…

Q: Compute the integral (3)/(1+x^2)-sec(x)tan(x)+2^xdx

A: The given integral is: ∫31+x2-secx tanx+2x dx ∫31+x2-sec x tan x+2x dx=3∫11+x2dx-∫sec x tan x dx+∫2x…

Q: Show that O tanh(In x) = x² -1 O (cosh x + sinh x)" = cosh nx + sinh nx %3D

A: From the given problem:   tanhlnx=x2-1x2+1   As we know that :   sinhx=ex-e-x2 ; coshx=ex+e-x2   So,…

Q: 3. Prove that: tan-1z = Z 2 in () i-z.

A:

Q: Prove tan-lz = Prove tan z= -j In j-z'

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: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = -2…

A: Differentiate the function f(x)=-2cos x-x with respect to x to obtain the value of f'(x) and equate…

Q: prove thatn f(x)=In(cosx), then f1(x)=-tanx

A:

Q: 2. Show that by using MEAN VALUE THEOREM 4-n < tan-1 v – tan-1 u < 1+v2 if 0< u<v 1+v2 3 <tan 25 -14…

A:

Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0,1 )

A: Concept: Trignometry inverse formula: One of the key ideas in mathematics is the inverse…

Q: Q4: Prove that: secx • cscx = tan x + cot x

A: According to guidelines we should have been able to solve only one question at a time #4

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Prove the identity 1+ tanz 1- tanz = tan (r

A:

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

A:

Q: Verify Rolle's theorem for: f(x) = e*(sinx - cosx) on

A: Given:

Q: 5- Show that a) sinh (z + ni) = – sinh z c) tanh(z + i) = tanh z

A: The complex function is of the form z=x+iywhere x is the real part and y is the imaginary part. A…

Q: Prove that : 1. Sinh'x= In(x+x² +1)

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: Find Maclaurin expression of f(x) = Cosh (x)

A:

Q: alue of x to

A:

Q: A-prove: (chose 4 only) 1-sinx 1. lim 1+cos2x

A: Q-1,1) Given- limx→π21-sinx1+cos2x=14 To Prove- The above expression.

Q: Prove that the inequality sinx+tanx&gt;2x holds in the interval (0,π2).

A:

Q: Evaluate the definite integral 27 3 16 sin (x)dx using Part 1 of the Fundamental Theorem of…

A:

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = 3 cos…

A: fx=3cos3x Differentiating with respect to x, we get f'x=3-sin3x·3=-9sin3x Now,…

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. (x2 - х) dx х2 +x+ 1

A:

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

A:

Q: Prove that? 2tanX tan 2X %3D 2 1- tan x

A: Given : 2tanx1-tan2x = tan2x

Q: - Show that sin converges. Hint: Use sinx <x for x 2 0.

A: Given: The series ∑n=1∞sin1n2, To show:  The given series is convergent.

Q: Prove the following identity (Sin x - cos x)^2 = 1 - sin(2x)  show work

A: Given: sinx-cosx2=1-2sin2x

Q: Prove that : 1. Sinhx= In(x+x² +1)

A:

Q: Prove that: tan-¹ z = In( 2 Note: tanz = And sin z = COS Z = ‚i+z. sin z COS Z eiz-e-iz 2i eiz te-iz…

A:

Q: Compute n Σ₁ tan(kx) tan((k+1)x) k=1 tan(nx) O a. + (n + 1) tan x b. tan((n+1)x) + tan x − (n +…

A: Trigonometric series

Q: Expand the function f(x) = x, 0 < x < 2, in half range sine series. 4 O (A) (#) = - sin()- sin() -…

A: