7) The integral that finds the length of the curve y = 1+ In(sec(z)), 0≤ ≤ [² tan(x) da (C) csc (2) dr (A cot (r) da (A) 7 (D) sec(2) (E) sec(z) tan(z) dz 8) The sequence a,, that is defined by a = √6a-1+7, a₁ = 5 is convergent. Then lim a, = da (B) (B) 5 (C) 1 (D) 0 (E) -1

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

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A: SOLUTION-

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A: We know that angle between two vectors a and b cos(θ)=a.b|a||b|

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A:

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A: Let's solve.

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A: We can find the integration using integration by parts as below.

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A: To find area of the bounded by the function.

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A:

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A: Here is the solution:

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A: To find the roots of the given equation D2-4(D-2)y=0

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A: The objective of the question is evaluate the derivative of the given function at given point.

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A: Express in p/q form 0.005

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A: The given integral is ∫3x2+4x3+4x+1dx

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Q: O False

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A: Velocity is obtained by differentiating the position function

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A: The objective of the question is determine the length of the curve given in polar form.

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A: ∫ln(x)xln(x)-xdx

Q: 2+3(4÷2)

A: Solving using BoDMAS rule

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A: Use fundamental theorem of calculus for finding the derivative

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A: To find out the double integration.

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