6.) value of sec o if tan o = - and o is quadrant II )3y +1

Q: aw Example 3: Find at „w=2ye*-In z , x=In(t² + 1) ,y=tan-1t &z=et

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Q: Graph the limaçon. Oval limaçons r = 2 + cos u

A: Given- r=2+cosθ To sketch- The graph of the above limaçon.

Q: 4. The area which is inside the circle r = 8 cos e and outside the circle r = 2 cos 8.

A: Introduction: In polar coordinate, the equation of a circle centered at the origin with radius a…

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Q: 25. What is the area of one of the petals of the rose curve r = 2 cos (20)? /4 /4 L con (20) do 8/"…

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Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: 11. Determine the values of n and h required to approximate e2r sin 3x dx to within 10-4. Use a.…

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

Q: (a) The averages of cos x and lcos x| from 0 to x are (b) The average of the numbers v,, the average…

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Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: ди ди 1. find az and " if z = 5 tan-1(x)and x eu + In(v) at the point (In2,1) %3D dv

A: Using chain rule.

Q: Find the area bounded by the trigonometric curves 5ñ to - 4 3.667 square units 3.459 square units…

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Q: 1+3x – cosI 2.) lim tan x

A: limx->01+3x-cosxtanx When we plug in 0 for x then we get…

Q: 2. Find the area outside the inner and inside outer loop of the limacon r = 4 sin 0 - 2 101

A: The equation for the Limacon is r=4sin θ -2 The graph given is

Q: Evaluate the integral tan 4x dx tan? 4x - 24 nltan- O inltan 4x + Vtan? 4x – 24| + C 1 Arcsec tan 4x…

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Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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Q: 4. Find the area common to the circler=3 cos 0 and the cardiod r=1+ cos0.

A: Find points of intersection and solve the given problem. A detailed solution is given below.

Q: Find the Residues of given points 1 at z = nt sin z

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Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

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Q: 1 Suppose y = tan ¹æ. Then x = y tan Otan y Oarctan y

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Q: 12. Find the area of the region shared by r = 1+ cos 0 and r = 1 – cos 0.

A: The given graphs are r=1+cosθ and r=1-cosθ We have to find the area of the region bounded by the…

Q: π 5π Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= —to x = 4 1.414…

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Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: du nd az and " if z = 5 tan-'(x)and x = e" + In(v) at tl-

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Q: Find the total length of an astroid x2/3 + y2/3 = 22/3, which can be parameterised as x = 2 cos³ 0,…

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Q: Find the areas of the regions . 1. Shared by the circles r = 2 cos u and r = 2 sin u 2. Shared by…

A: 1. Area of the region shared by the circles r = 2 cos u and r = 2 sin u Replace the variable u by θ…

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

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Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: The value of the integral (s cos (r) dr is S COS Select one: O s(cos(2) – cos(0)) -

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Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: 2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos…

A: To find the distance between the two points

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: Select the definitions of sinhx, tanh a, and sech z. O e +e- e -e-z O e-e e +e-z O e -e e +e- O e +e…

A: The hyperbolic function of sine is expressed as-     sinh x=ex-e-x2 Thus, Option (C) is the correct…

Q: 7. Prove: (a) sin iz = i sinh z. (b) | cos z|? = cos² x + sinh° y where, z = x + iy. COS

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Q: 2. By using Simpson's rule with N = 4 , 8 , and 16 Integrate the following functions et [0,1] а. Tan…

A: Simpson's Rule: S =h3 fx0 + 2∑j=1n2-1fx2j +  4∑j=1n2fx2j-1 + fxnWhere, h = b-ana = initial limit, b…

Q: (§5.7, Q98) Show that the two regions in Figure 4 have the same area, i.e., show that V1 – x² dx :…

A: We have to show that  ∫011-x2 dx = ∫0π2cos2u du.

Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

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Q: The base of a three-dimensional figure is bound by the graph x = sin(y) + 1 on the interval [0, π].…

A: We have to find the area of each triangle.

Q: Which of the following is true? @ Ssin*(x)cos³(x)dx = - cos°(x) , cos®(x) cos(x) cos °(x) 6 4 10 ©…

A: answer of A:    Answer of B:

Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

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Q: 213 If cot 0+ tan = and sece - sece = y, Prove that (x'y)° (xy²)*° = %3D

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Q: The area between the two loops of the limacon r = 1+2 sin 0.

A: Question- The area between the two loops of the limacon          r = 1 + 2  sin theta .

Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

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Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: Let fcx) = cos(x) at X , X - 11 and X=1.2 Ues Lagrauge iuser polaling poly to oppro Ximete

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Q: 1. Find the areas enclosed by the x-axis and the following curves and straight lines: с. у%3 sin 2x,…

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Q: HOW DID HE GET THE VALUE INSIDE THE CIRCLE cos² x D²+1 For given particular integral multiplying and…

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