20. Simplify the expression o con z- sin z-1 tan z O - sec? z O - tan? z O sec? z

Q: Which of the following represents a correct substitution used to compute: a2 da 4 sec2 (0) de a) O…

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Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: 41. Show that if u = tanh(x/2), then 2u 1+u? 1- u?' 2du 1- u? cosh x = sinh x = 1- u? dx = Hint: For…

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Q: If f(x) = 3 tan¯¹(6 sin(4x)), f(z) = Question Help: Video

A: Given that fx=3tan-16sin4xTo find :Derivative of fxSolution…

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A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

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Q: If f(x, y) = x cos y, then fry(0, 1) = ? Select one: O 1 -1 O None of them sin y

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Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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Q: The suitable substitution to evaluate the integral /tan°(2x) dx is cos“(2x) O u= tan(2x) O u=…

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Q: Let 3 sin z+ 6 cos y= 4.

A: The first derivative of y with respect to x is given by the expression . The second derivative of y…

Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

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Q: cosh? z + sinh2z=1 true False O оо

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Q: Suppose sin u=x and u is between 0 and 2. What is cos u? V1-x2 | VI- 2² 1

A: Consider the following equation: sinu=x Consider the following trigonometric identity:…

Q: i) um asinx-sin2z ,u fünute, fünd the vaue the uimit. tana ofa and

A: Now, the limit is finite given so, the above must be 00form So,  a cos0-2cos0=0⇒a-2=0⇒a=2

Q: For x >0, tanh(Inx)+ dx x2 - (tan-(x)) 1 + > = x? .2 Select one: O True O False

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Q: 8. Convert all expressions in (a-<) to a form A (x)+ B (x) dxteNote that A and B will vary from <ase…

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Q: Evaluate: x tan x dx 3 A. – In /2 – 4 32 B. -1- 4 32 V3m _ In 2 – 5 3 18 D. NO correct choices. C.

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Q: 3. / sed into something with tanh (r) then let u = sech (r) (Hint: break up into sech (r) sech (x),…

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Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: Evaluate S(cos?y – sin?y – csc 2y)dy O -sin 2y + In|csc 2y – cot 2y|| + C O sin 2y – In|csc 2y – cot…

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Q: 4) S(tan³ z + tan z)dr = a) tan z+tan? r+C b) tan? r+C c) In sec z+ sec? z|+C d) tan z+In |sec r|+C

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Q: If sinh x =tan t, 0<t<3/2 , then tanh x = sin t. Select one: O True O False

A: We have been given  sinh x= tan t for 0&lt;t&lt;3/2

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…

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Q: Which option equalsS x sec2x dx ? Exactly one option must be correct x secx tanx - In(cosx) + C O x…

A: Hence option (b) is correct.

Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: 4. Evaluate r³ sin r). dz

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Q: Which expression is equivalent to O cotx+sec x O cos x + cot a Otan x+sec x O sinx+tan x an £ ? cos…

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Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: tan e lim is 3 5 sin e O a. 1 5 O b. 5 Oc -1 O d. o

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Q: Prove the following i. ii. 1- sin x 1 = sec x – tan x. cosec e + sin x, V(1 – cos? 0)

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Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: Evaluate: sin z -dz +(°z – z)

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Q: The suitable substitution to evaluate the integral tan (2x) dx is cos“(2x) none O u= csc(2x) O u=…

A: Given: ∫tan52xcos42xdx

Q: 8. Evaluate (a) /sin z cos" z dr (b) / (ln z)* dz. You may use /In z dz = z ln z - z+c.

A: Let's find.

Q: Assume that x, y ER and z = x + iy E C and answer the followings: 1. Evaluate sin(i) =?, cos(i) =? ,…

A: Since the questions contains many subparts as per the guidelines I am answering the first three…

Q: 22. Determine Sz sin? y cos y dy

A: Given that: ∫0π2sin2ycos6ydy

Q: Evaluate: sin z dz +(°z – z)

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Q: 4)/caso+i)de; let x be const ant a)cin Ceti)+c+x A) -sm (cH) rc -in c.) -sin(c)+c a.) sin (c) + ct X

A: Let's find integration of given function.

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

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Q: Homework: 1. If y=tan x, prove that y`= 2(y +1)(3y² +1).

A: As per the guidelines I solve your first question. For more solutions please resubmit the question.…

Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: Evaluate. S cos z In(sec z)dz Your Answer: In(sec z) sin - In tan z + sec + sin z + C

A: Please see the answer below.

Q: /hich of the following statements is true? +C (x-5) In(3) B dr=sec-!(x) +C tan²(x) dr =tan(x) – x +…

A: We are going to solve

Q: dx Evaluate / 25+7x2 V7x + C -1 tan O None 1 V7x tan- 25 + C 25 1 tan V7x + C 7.

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