4 CX ) = (T-X) く) Xスズ find The half e Range sine ond cosine servies k1コ

Q: Find the quadrant in which the terminal point detemined by t lies. sin(t)<0 and cos(t)<0…

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Q: 5. Find : 60 y= (b) y = cos (11x³ + 5x). dx

A: SOLUTION-

Q: Express æ = 3t, y = tan-'(t4 + e') in the form y = f(x) by eliminating the parameter.

A: Given : x = 3ty = tan-1t4+et

Q: 4T then 3 If 0 = sin(0) = %3D Give exact value.

A:

Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

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

Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

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Q: 1. 2. (D² -3D+2)y=sine-*

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Q: The x2- 4 dx can only be evaluated using trigonometric substitution technique . A True B) False

A: To find if the given integral can be solved only by algebraic substitution technique.

Q: tan 0 d 30. dO sec² y dy

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Q: The x² – 4 dx can only be evaluated using trigonometric substitution technique . A) True B False

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Q: Find the period of the function y = sin(2x + 1.5). %3D 2 2 2л

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Q: Q Is the equation e + x cos x 2 = 0 has real roots?. -

A: To show there are real roots, just use intermediate value theorem on appropriate interval.

Q: Q1: Find the X- Value of the Trigonometric Equation. 5 sin nx - 7sin nx. cosnx + 10cos nx= 4

A: Given, 5 sin2nx - 7 sinnx . cosnx + 10 cos2nx = 4 To find the value of x, The given equation can be…

Q: If y = -cos(2t), then y(5)= ?

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Q: find the inflection points at y=4x+sin8x​, −pi/6≤x≤pi/6

A: Inflection point  is a point where second derivative changes sign. a) If f''(x)>0, then f(x)…

Q: 26) y = tan((T/6)x) Period: TT. -217 -ㅠ TT 21T -2 -1 -1 -2 -ㅠ MCL @01 %24 ElN-

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Q: Obtain the general solution to the equation. dr +rtan 0=7 sec 0 tan e de

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Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

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Q: r = -4+4 sin 0

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Q: Find the equation of a cosine wave that is obtained by shifting the graph of y = cos x to the left 9…

A: Please see the answer in step 2

Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: b. What is the range of y = sin-12x? %3D

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Q: d) Use Newton Raphson method to estimate the root of cos x-xe* = 0, initial guess is

A: To find- Use Newton Raphson method to estimate the root of cosx - xex = 0, initial guess is x0 = 1.

Q: .3 Use Trigonometric Substitution to evaluate: dx 2 |1+4x²

A: This question is based on indefinite integral.

Q: What is the dependent variable in the equation dr + (2rcot0+ sin 20) d0 = 0?

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Q: 3. f10x-sec(5x) tan(5x²)dx ans : sec(5x²) +c (VF). cot 4. dx ,note: Vx = xr ans : 2 In

A: ∫10x·sec(5x2)tan(5x2)dxlet u=sec(5x2)du=sec(5x2)tan(5x2)·10x  dxdx=dusec(5x2)tan(5x2)·10x Replace dx…

Q: The velocity, v ms-1, of a fairground ride t seconds after it begins is given by v = (3e-t + 7)sin t…

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Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

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Q: cos ax -dx = te' 2 х* +1 ле",а 20.

A: In this context, prove ∫-∞∞cos axx2+1dx=πe-a,a≥0. Consider, ∫cfzdz=∫-∞∞cos…

Q: -2.2 Use the Trapezoidal rule to approximate CoS dx with n = 5.

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Q: Q6. (A) Compute S[sec* (÷) – 1] sec")dx . (B) Use Trigonometric substitution method to evaluate fe…

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Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOL'N): у%3D 3…

A: given that y=3 arccos1-x3+6x-x2 find the second derivative of y

Q: Q6. (A) Compute S[sec² (÷) – 1] sec*)dx. (В) Use Trigonometric substitution method to evaluate…

A: We will find the integrations as following.

Q: -31 cosh 2t 7. (a) 2e- sinh 3t (b)-

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Q: 4. xy = COS (²) + +1

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Q: Use trigonometric substitutions to find dx. V1-

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Q: What is the value of k so that dx sin(kx2) = 6xcos(kx²) ?

A: Topic - derivative of a function

Q: c. Find approximation of the value cos(65") with error less than 5 x 10-5.

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Q: 15 Find the Equation of the tangent at (); 4 2 'V or to armist mi Y sin (127) = x cos (24) 7 ition]…

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Q: cos(4x) dx - Find the Cauchy principle value (showing details): J (+5x2+4)

A: Given integral is, I=∫-∞∞cos4xdxx4+5x2+4 So, the function is, fz=cos4xdxx4+5x2+4 Now, consider the…

Q: What is the range of the function y = sin-1x? Select one: 2' 2 (-플, 끌) 2' 2 O [-1, 1] O [0, 1] 프2 프2

A: Given function is y=sin-1x

Q: Q3- i) Prove that -cos-lu = 1 du dx V1-u2 dx ii) Find the angle of inclination of the line y + 2x –…

A: we have to show that the following.  And find the angle of inclination of the line y+2x-4=0

Q: Q2) a) Find an® sec²y dy b) Is cos4xv2-stn4x dx = (2- sin4x) +Ctrue or false? show me

A: Use fundamental theorem of calculus for part (a)  For part (b) use substitution method

Q: Find the tangent of 2X. Х. 13 Y 12 Write your answer as an integer or as a decimal tan (X) %3D 5.

A: this is the right triangle

Q: (7/6 sin t dt cost 39.

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Q: y 3x+ 6 cosx, 0 £xs 2n

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.