> fnd period of 8- tan 4x 10 2 y. 5 Cos 10* 11 12 → Skekch these funchion 3- 13 14 1 ys 3Sin (X +T) 3. 15 16 Cos X + TT 17

Q: 13. To evaluate f 3cos*x-1 dx. the integrand can be transformed to 1-sin2x a. [(3cos x+ csc²x)dx b.…

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Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

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Q: 1. f(x) = sin 2x + cos 3x + x² = 0 with xo = -0.5 , Ax 0.1, TOL = 0.001, in [-0.5,1] %3D

A: Given equation is fx=0 where f(x) is defined by fx=sin2x+cos3x+x2  Given initial solution is x0=-0.5…

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: The position at time t ≥ 0 of a particlemoving along a coordinate line iss = 10 cos(t + π/4). What…

A: The position at time t ≥ 0 of a particle moving along a coordinate line is s = 10 cos(t + π/4) We…

Q: The slope of the tangent line to the curve r=cos20 at 0= 1/4is none of these O-V3 0 1 O (-1)/V3

A: As we know that; The slope of the tangent line to the polar curve at the given point is equal to the…

Q: The prolate cycloid given by x = 2t − π sin t and y = 2 − π cos t crosses itself at the point (0,…

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: 4. Show that f(x) = sin(x² + 3x) is equal to g(x) = -x cos(x) at least once on %3D Hint: Think about…

A: Given that, f(x) =sin(x3+3x),  g(x) =-xcos(x) Given an interval as -π,-π6 To show that f(x) and g(x)…

Q: 11 Evaluate (( sin(y²)dydx where 2: 0<y<1, 0<x<y. 0 x a) 1-cos(x) b) 1-cos(x)) 1 - cos() 2 d) 1.…

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Q: 9 If f(0) = cos 0 · cos 02 cos 03 ....... cos 0n %3D f'() + tan 0,}=- f (8)] Show, {tan 0, + tan 02…

A: Introduction :

Q: (3+ 7cos (x)) sin? (x) de 28. 29. sin° (9y) sec² (9y) dy / tan" (2) cos" (2) dz 30. [tan(2t) – sin°…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: A particle moves along the x-axis with position given by x (t) = -2 cos (2t) + 2 for time t > 0.…

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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: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

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Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

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Q: Determine the area between the curves y = 9 + 7 sin and п y = -7 -9 cos 3 on the interval -9 s x <…

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Q: 3. Solve the IVP: siny(x + siny)+2x²cosy y'=0; y(-1)= π/2 (Subst. first and then Bernoulli's)

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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: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

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Q: D. 1. If (x + y)² = x² + y² 2. If y = sin³ () cos³ () dy - dx X prove that y' = sin² (x) cos(x) 8…

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Q: 6. f(t)=-e" sin (2r + 7) -2t 7. f(1)= 3e " cosh (In 21) %3D

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Q: 3Tt of cSC X du If u = f(x), then dx cos X . Compute %3D 2 sin x и -

A: Given ,  u = f(x)

Q: Integr S√₂-cod -1 ation fuctions. 1-cos²x) dx Not of the above B 1 O

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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: я/4 4 sin (4t) dt. 9- cos (4t) Evaluate the integral я/4 4 sin (4t) dt%3D 9- cos (4t)

A: Use integration by parts

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

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Q: 4. The given equation sinh(xyz) = x + y + 3z implicitly defines a differen- az tiable z as a…

A: Differentiate with respect to x keeping y as a constant.

Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: A string is stretched and fastened to two points at a distance 'x' of 10 cm. Vibration is started…

A: The given problem is to show the displacement of initial shape of the string from the given…

Q: 4. tanx dy + y3 sin? x dx %3D 0, whe х %3D0, у%3D 1 о у?(3- сos 2x) %3D2 о у (сos 2x - 2x) %3D 1 о…

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Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

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Q: 2. Locate the first positive root of f(x) = sinx + cos(1 +x³)- 1 where x is in radians. Use four…

A: (a) We need to find the root between 1 and 3

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: a3z cos(x – 4y) show that a3z 6. For z = дудхду

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Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: 3. f(x,y)= In(x cos y)-cos (In3y)+

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Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

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: derrivative of: Cos(xy)+secy=5

A: Consider the given expression as cosxy+secy=5

Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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Q: 9 If f(0) = cos 0 c • cos 02· cos 03. ... cos On f'(0) Show, {tan 01 + tan 02 + tan 03 + ....+ tan…

A: We have fθ=cosθ1·cosθ2·cosθ3....cosθn                 ....(1) Now, we have a formula…

Q: 1. Determine the smallest positive root of f(x) = Sin x + Cos ( 1+ x ) - 1. Use 5 %3D iterations of…

A: Given function is f(x)=sinx+cos(1+x2)-1 the graph of the function is From the graph we can see that…

Q: 4x – 1 for the 2 tan(4x-1)-3 cos² (4x-1) dr. what will be the resulting integrand? If we let u =…

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