We consider the following 2n-periodic function f given by Jо, if —т <х <0, lx, if 0

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A: As we all know the theorem which states that, For z∈ℂ\ πℤ 1sinz=∑n=-∞∞-1nz-nπ=1z+2z∑n=1∞-1nz2-n2π2…

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Q: (A) Evaluate Sin (3x) Sin (3x) dx

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A: Please refer to the image below.

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Q: 110. π/3 -π/3 /sec²x - 1dx

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

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Q: Newton - RaphsonMethed Lnlx-1)+ cos(メ-L)=o P(xn)laーメn

A: The formula to find the next iteration according to Newton's method is:

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

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Q: 7. Prove that d dx [cos ¹ x] = = 1 √1-x² x2

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Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: EVALUATE -dx + 144 ,2 O x – 12tan-1 12 none 1 -sin' 12 x – -1 +c 12 O x – tan-1 12

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Q: 20 1 [25 — Зг]sin(птх/20) dxt. NTI 10

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT yyy Ü♥¯ ¶ ☆ @ ! ! ?? !! ? ?! ¿ ¡ !? S❀ W X Х Х Х Х A * ✓✓✓ DO -…

A: We have not any digital tool .

Q: sec−π/3

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Q: Using the substitution t tan can be written as of dx sin(x) - 60 cos(x) of dt +30-30 2 de 30²2²…

A: I am attaching image so that you understand each and every step.

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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)

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Q: Find the sum of the first 8 terms of a geometric series if the first and second terms are 1 and 12…

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Q: -> (6) 금 AxB) at t-1 at t=1 (1) A X 4P

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Q: Evaluate i) A (x +e* + 2) _ii) A sinh (a + bx) iii) A cosh (a + bx).

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Q: 71. Use Figure 4 to prove V1- 12 d /1 – x2 + sinx FIGURE 4

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: