Activity 2 Find the first derivative of the following: 1. y = ln (12x) 2. y = sin-¹ (x² + 3) 3. y csc-¹ (4 - 5x) = 4. y = ln (100x)

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A: We have to find the truth table for the given compounded prepositions.

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A: Let's find.

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A: find limit using L hospital rule option C correct answer

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Q: ∫sinx sin(cosx) dx

A: ∫sinxsincosxdxLet u=cosx=∫ -sinudu=-∫sinudu=--cosuSubstitute back u=cosx=--coscosx=coscosxAdd a…

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Q: 2. Find the laplace transforms 3. Find the laplace transforms of f(t) = et³ of f(t) = ¹e²t (2t)

A: Note: There is no standard form of Laplace transforms of f(t)=et3. For (3),     L14e2t2t=14·…

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A: topic - Area between the curves

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Q: Question Evaluate the indefinite integral given below. [ (sin³ (sin³ (x) - 3 sin² (x)) (sin (x) — 4…

A: Given,             ∫sin3x-3sin2xsin4x-4sin3x6cosxdx

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Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

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A: We will put Revenue=0 to find the value of x

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Q: 1. If g (2) = 59 and fg'(x) dx = 25, what is g(5)?

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

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A: Since you have posted multiple questions i can do first question as per our company guidelines

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A: We need to find surface integral.