2. i) Find in radians the values of x in the interval 0°< x <360° which satisfy the dquation cos2x - sin2x = 1. ii) Find in radians the general solution of the equation cos5x + cos3x=0 iii) Express cosx-v3 sin x in the form R cos(x +2) where R>0 and 2 is and acute angle. Hence find the maximum and minimum values of: -cosx-V3 sinx.

Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

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Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: 2. Evaluate the integral ſcos (3x) sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: 1 - / sin2r - ycos2r điferansiyel denkleminin genel çöztumt aşağıdakilerden hangisidir? a) Hiçbiri…

A: Consider the homogeneous differential equation y'sin2x-ycos2x=0. Variable separable form:…

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Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

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Q: B\ Suppose that = 4 cos? t , x = v3 sin(2t) and 0 < t < n. S d²y *= - tan(2t) and = -sec (2t). 1 dt2…

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Q: If x = sec e - cos e and y = sec" 8- cos"0 (x² + 4) (* - n°(y² + 4) = n²(v² + 4) Prove or disprove…

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Q: Given that Y1 = x-1/2 cos x and y2 = x-1/2 sin x from a fundamental set of solutions of (--)- x²y" +…

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Q: x³y"+xy'+4y = cos (2 In x)

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Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

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Q: What substitution should be used to solve the integral x²dx |4+9x² O sin u=3x/2 sec u =2x/3 O sec u…

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Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

Q: Find !V1-cos xdx 2 sin x = 1- COS X V2(-cos x/2)+ c 1/ /2(-cos x/2)+ c В. 2/2(-cos x/2)+ c С.…

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Q: Consider the following IVP: y" + y' = -cos x; y(0) = a, y'(0) = b Find the general solution. y(x) =…

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Q: Solve the given differential euation: dr/dθ+rtanθ=10cosθ. 1.r=(10θ+C)tanθ 2.r=(10θ+C)cosθ…

A: In this question we have to solve the given differential equation.

Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: 2) If the secant method is used to solve the equation xe" cos(2x) = 0 in [0.7,0.8] then the vahue of…

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

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Q: 1. Solve the DE tan x sin y v + ( 3tan X -2 cos y) sec'x=0

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Q: 7). Suppose a is a positive constant less than T. Prove that the equation 2x+cos x = a has a real…

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Q: 4. Derive error-bound formulas for the following expressions. i) cos(x) – sin(x) ii) In(x) + sin-1 y…

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Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: What is the particular solution of the function 2xe3 sin 7x – 8x?? O Aa? + Bx + C + Exe3, cos 7x +…

A: NOTE: Refresh your page if you can't see any equations. . . the second function is  which is a…

Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

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Q: On what interval is the solution of the IVP cos e (1+ sin 0) y (0) = 2 - 47 valid?

A: Given IVP is dydθ=1cosθ1+sinθ y0=-12 Now,  dydθ=1cosθ1+sinθ dy=1cosθ1+sinθdθ∫dy=∫1cosθ1+sinθdθ

Q: 7 Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 2 = sin z+1 has a…

A: use the intermediate value theorem and Roll's theorem to show that the eqautionx2=sinx+1has a…

Q: 2. Evaluate the integral (cos (3r)sin (3x)dx in two ways, one with u = sin(3x) and the other with u…

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Q: Find the first approximation to the root of the equation xe" – cosx =0 using Regular-Falsi method…

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Q: () = 2 + Solve the initial value problem : f'(x) = cosx + sec?x, %3D

A: As you post multiple questions we only solve first question only.

Q: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

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Q: The solution of the DE (1+ tan x)y'=-secx coty is O None of these siny + In cosx| = c %3D sinx +…

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Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

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Q: (5) Use the Intermediate Value Theorem to prove that xe* = cos(x) has a solution.

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Q: 10. Solve for t on the interval [0, 2π) (a) 2 cos² t-cost-1=0 (b) 2 sin²t-3 sint + 1 = 0 taol al (c)…

A: Given

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Q: Given: z = sin 3x cos 4y Find: z ду2 -3 cos 3x sin 4y -9 sin 3x cos 4y -12 cos 3x sin 4y -16 sin 3x…

A: Differentiate the given function partially w.r.t y keeping x as constant   ∂z∂y=sin 3x×4-sin 4y…

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Q: Find all solutions to the equation: [sin(x)+ 1]2cos(x)-3]=0. Зп + 2nk, x = + 2nk, x = 11m + 2nk,…

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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: Given: cos 3y + sin 2x 2 cos 2x 2 O -3 sin 3y-3 -2 cos 22-2 O -3 sin 3y 3 O -2 cos 2x-2 3 sin 3y 3 2…

A: Given: cos3y+sin2x=2x+3y To find dydx in the given equation.

Q: Find y, of 2 -3+2y 6 cos x+9 sin x dx ... a.) y, = 3 cos x+ 2 sin x b.) y, = 3 coS x- 2 sin x c.) y,…

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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: 9 If f(0) = cos 0, cos 02 cos 03 ..... cos 0n %3D Show, {tan 01 + tan 02 + tan 03 + ... + tan 0,} =…

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Q: 16. So the maximum occurs at an angle of 0, but only if the angle is small enough. Explain why that…

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A: We have to find the necessary equation that must be satisfied.

Q: b) Is S cos4xV2 – sin4x dx (2 – sin4x)³ + C true or false? show me

A: this is false because

Q: 8. Find the positive root of the equation 3x - cos x - 1 using Regula Falsi method and correct upto…

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

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.