(a) | Show that tan- z = in() = n 1, і —z i + z -In i - z -In z +i %3D | - (b) values of tan-(2 + i). ] Use part (a) to find all the

Q: Q: Prove the following identitie: (1+tan A tan B) +(tan A - tan B)* = sec' A sec' B.

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Q: +siny+x

A: Side View

Q: -1 a) y = x tan 2x 4 4x +. b) In(x+y)=Dtan (xy) c) y=e* cos x d) x +xtany = e e) y = Vz sin (z)

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Q: Evaluate the integral 1/3 El+ secx tan x dx

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Q: Evaluate: Sin (sin ²¹ (2) + tan ¹ (-3)

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Q: x-1 c) Let f (x) = x+ 0. Find by using numerical calculations in a tabular x2 - 1 which x approached…

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Q: f(seca tan a – 8a")da tan a + a° + c sec a +a8 +e - sec * – a8 +c sec a – a° +e sec a +8

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Q: (1 point) Find the area inside the cardioid r = 2 + 2 cos 0 for 0 ≤ 0 ≤ 2π. Area =

A: Step 1: Step 2: Step 3: Step 4:

Q: x) = sinx and g(x) = In x a) What is (f o g)(x) ? b) What is the domain and range of (f • g)(x) ? c)…

A: According to our guidelines we can do three subpart of a question at a time. Please post remaining…

Q: a-X Tan" 1+ ax Differentiate

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Q: 3. ſsec? x(1+ tan x)/tan x – 1 dx ans : 3 (tan x – 1)' + ¿(tan x – 1) +c 4. S'cos x(2+ sin x)/2 +…

A: 3. Given integral is ∫sec2x(1+tanx)tanx-13dx Substitute tanx-1=z⇒tanx=z+1sec2xdx=dz Therefore, the…

Q: 1 /₁+422da dx 1+ 4x2 15. Evaluate (a) tan-¹(x) + C (d) tan-¹(2x) + C -1 (g) tan-¹(x) + C (j) None of…

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Q: 5. (a) 1 6. (a) The amplitude of the function y=4sin(x+ë)+1_is (b) 4 (c) 5 The horizontal…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: n lim >(sin (2mx;))Ax over [0,1] i=1

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Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

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Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: Given that z = 1- iv3, express z in the form r(cos 0 +i sin 0). Hence write down z' in the form…

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Q: Deseribe the transformations applied to y = sin x to obtain y = 2 sin(3x+5) + 1- %3D

A: y = sinx ---> y = 2 sinx,  The graph is stretched along y axis by a factor of 2   y = 2 sinx…

Q: w wor

A: Here we have to evaluate I=∫ln(sin(x))cos2(x)dx ...................(1)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.