Which statement is TRUE about trigonometric functions? O a. The derivative of sin x, cos x and tan x are negative functions. O To get the derivative of trigonometric function csc 5x,we need to use the chain rule. O To solve for the derivative of 5sec4x, we need to use the product rule O No correct answer O The function tan x has a derivative of sec x tan x

Q: y" + 4y = cos²x

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A: Here we have to use the concept of derivatives.

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A: To find the compound interest.

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A: As you have asked multiple questions so that I have answered first question as per the guidelines.

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A: improper integral means whose limit at any point goes to infinite  here check for it. ∫1dx/(x-2) =…

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A: Let's find given integral.  We there is lower limit not given but it only possible 1.

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Q: 6. ၂ 3z+1 -4) -dz

A: ∫3z+1(z2-4)2dzExpand:=∫3z(z2-4)2+1(z2-4)2dz=3∫z(z2-4)2dz+∫1(z2-4)2dzNow solving…

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A: We have to find limit

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Q: 20. √9-5x² X -dx

A: SOLUTION-

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A: The given integral,        ∫6x dx

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Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

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A: This question is based on gradient of function.

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A: Solution of given question is written in below steps.

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A: Integration

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A: Solve the following

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A: Given: I=∫7x4-16dx   As we know the common integral. ∫1ax+bdx=1alnax+b+C And ∫11+x2dx=tan-1x+C

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Q: Q1/A) Replace the polar equation by equivalent Cartesian equation r2cose +2sing

A: I am going to solve the problem by using some simple calculus to get the required result of the…