2. Show that by using MEAN VALUE THEOREM. u-v < tan-1 v – tan- u < if 1+v2 A>n >0 1+v2 3

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

A:

Q: Let f (x) = 6 sinh 1(tan(x) , O < x < 5. Find the slope of the line tangent to the graph of f at the…

A: Given: Here, we need to find the tangent line to the graph of f at the point on its graph where…

Q: 18. Use periodicity to express sec in p given that sin

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

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A:

Q: 3. y" +y = 2 cos x - sin x; y = x sin x+ x cos x

A:

Q: Calculate value for  sin((j*pi)/2)

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Q: Determine the range of f(x,y)=tan 2+x +y

A: Here the value of x2+x2+y3 can vary from -∞ to ∞. The possible values of tan-1x2+x2+y3 is…

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A:

Q: 3 Consider the function g(x)= sin --1| with restricted domain [0,4]. Find and identify any relative…

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Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Let f(z) = 4 cos I-3 tan z. %3D S(2) =D %3D

A:

Q: 18 a Show that / (1 + sin 2zx)dx = n, for all positive integers n. b Sketch y = 1 + sin 27x, and…

A:

Q: 3. Consider the function f (x) = sin² x + sin x on the interval (0,2n). a) Find the open interval on…

A: The given function is fx=sin2x+sinx on the interval 0,2π. a) Obtain the first derivative of the…

Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

A:

Q: 4. Evaluate tan (4.3 – j1.1).

A: Given that, evaluate tan (4.3 - j1.1).

Q: Choose true or false of the following 1- S, x? = 1 2 %3D 3 2- J sin x dx = 2 3- Se* X² dx = xeX + c…

A:

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

A:

Q: 10. Integrate the function. 8 ip- 1+ 641 2 sin" 8 2 2 tan- 8 2 tan" 8

A: We have find the integral.

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

A:

Q: S Sech (ax-

A: Evaluating the integral of hyperbolic function using substitution.

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: dv Integrate 9 + v2

A:

Q: What is the trigonometric substitution that you would use to evaluate the integral S V5x2 + 10x +…

A:

Q: 2. Prove the following identities. = tan (x+2) 1tanr 1-tanx b) sin(π-x) - tan(-x) = sin2x c) secx =…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Q/ Evaluate the following functions 1.In(3-16) 3. cos ¹ (1+i 3) 2 (3|0.52) 2. e ‚4. tanh¯¹ (2-i5)

A: According to the given data, evaluate the functions:

Q: 7. B- Show that: (1) lime-0 tan 8 (2) tan 0 sec20 =D1 %3D do

A: Solve

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A: Find the Maclaurin expansion of  f(t)= cost

Q: ) Find the derivative of the following: a) sin (4x- 7x+ 3)

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Let f(x) = – 3 sin( – 2x – 5) – 6?

A: