Problem 2 Which of the following sets are linearly independent? Prove your assertions. {(-12 1) (1 1). (1 3). (²4 4)} " (2) {x³ + 2x²,-x² + 3x + 1, x³ – x² + 2x − 1} in P3(R). (3) {cos²(x), sin²(x), cos(2x)} in C(R, R), where C'(R, R) is the set of all continuous function on R. in M2₂ (R).

Q: 4 1) Given the function f (x) = 5 – 2 cos f(-) 3T a) Find the exact values of f () and f(-4) b)…

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Q: aluate ㅠ - π 2 cos² (9x) dx.

A: Remember :  cos(2x)=2cos2x-1⇒cos2x=1+cos(2x)2 we have to find  ∫-ππcos2(9x)dx

Q: Compute S x? cos(x³ + 3) dx

A:

Q: 5. What is the exact value of cos(™)? y (0, 1) (二) (-1,0) 号 O 0号 01 19 () (-²,-²) )。 at trafte 135°…

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Q: Show that M8 Σrk k= pk cos(ak) = −1+ 1-2 2(r2-2r cos a+1)

A: Using summation of infinite series in geometric series Sum = first term /(1- common…

Q: 5. Compute y" where y = cos² (2x + 1) O-4 sin(2x + 1) cos(2x + 1) 08 sin² (2x + 1) − 8 cos² (2x + 1)…

A: Given function:- y=cos22x+1

Q: 3 then evaluate sec(-t – 27). 4 (b) Givem cost --

A: We have to find the value

Q: 7. y - 5y"" + 7y" - 5y' +6y=x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C4 sin x + x² + ²x - 3/4

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Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

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Q: 6. f cos³x√sin xdx)

A: sin2x+cos2x=1∫xndx=xn+1n+1

Q: How many distinct solutions does the equation sin(3x) = have on the interval [0,27)? 2 (A) 1 (B) 3…

A: Sine angle is positive in first and second quadrant only. Also,  To solve any trigonometric…

Q: Evaluate fa² tan³ (2³) da + C

A: To integrate the given  function.

Q: 2x 2)/3x* 2) [3x* - 9x² +1 V9-x² dx .2 3) [ sin xcosx dx x cos.x 4) S sin² xcos 4) sin x cos x dx

A:

Q: 2) Evaluate: x* cos(x 5) dx. (A) 1/4 sin(x 5) + C (B) 1/5 sin(x 5) + C (C) sin(x 5) + C (D) 1/5…

A:

Q: x 16. Evaluate sin dx. f x +C O O- 1 3 cos³x 1 3 cos³x 1 2 cos²x 1 O- + C +C + C 2 cos²x ONone of…

A: we have to slove above integrate