power series representation for x³ s(2²) dæ ° cos (x

Q: standard

A: As per the guidelines we can solve 3 parts only. Please repost the same for more answers.

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Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

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A: Explanation of the answer is as follows

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A: Let, the number is x. The sum of the number and the square of one less than the number, S=x+(x-1)2

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A: x ex2 dx + (y5-1) dy =0x ex2 dx =(1-y5) dyvariable separable;∫ x ex2 dx=∫ (1-y5) dyx2=tx dx =dt212∫…

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A: Substitute the values given in the options and verify.

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A: ANSWER: OPTION 2nd

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A: This question is based on 3d line equation.

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A: Find your answer below

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

Q: 11 2

A: We can solve this as follows:

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A: To solve the given differential equation.

Q: What is/are the critical number(s) of the function S(2) = +4, f(z) :

A: f(x)=x2+4xDifferentiatef'(x)=x2x-x2-4x2f'(x)=2x2-x2-4x2f'(x)=x2-4x2

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