DISCUSS THE PROPERTIES OF THE CURVE AND SKETCH FULLY (drawn to scale) 1. y x- 3x2 + 4x- 12 2. y = (x² – 5)2

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A: Please refer to the image below

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A: solution:-f'(x)=ln(x2+1)f(x)=∫ln(x2+1) dxusing integration by partsf(x)=∫1·ln(x2+1) dx=ln(x2+1)∫1 dx...

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Q: This situation below applies to the next four problems A bacterial colony is cultivated in a petri d...

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Q: d²y 1. 5 dx - 6y = 0 y(0) = 2; y'(0) = 4 - %| dx² d²x(t) 2. ·+ w?x(t) = 0 dt2 x(0) = A; x'(0) = vo %...

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

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A: Answer :-  Given limit x tends to π then cosx is what.

Q: 13. y = e* Sin-1x + Sin-'x] O c. e* a. b. b. e* [ Sin-x] d. e*- + Sin 'x]

A: use formula of differentiation of products of two function 

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Q: 10111111110 110101

A: Solution is 10011110110010110

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A: This question is based on Indefinite integration.

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A: E) z=exSiny.

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Q: y = e2x+1

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A: Explanation of the answer is as follows

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A: Let's find. 

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A: Given that ∑n=19∞8n3-3n2+195+3n4Use limit comparison test

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A: Given, f(x)=x2/(2x+4)

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A: The given question has been solved in detail

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A:  If limk→∞uk is nonzero, then the series ∑k=1∞ukis divergent.

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Q: 1. Use a direct proof to show that "If n is an odd number, then n' is an odd number."

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the anothe...

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A: Give curve,         y = 8x-3x² at point (2,4)

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Q: Show that f(x, y) = e2x cos(x + In y) satisfies the differential equation 2f - yfyx = 5f.

A: Given that fx,y=e2xcosx+lnyShow that 2fx-yfyx=5f