State in interval notation where the graph is differentiable. A) (-∞, -1) U (-1,3) U (3,00) B)(− ∞, −3) U (−3,−1) U (−1, ∞) C) (-∞, -3) U (-3,-1) U (-1, 3) U (3,0) D) (-∞, -3) U (-3, 3) U (3,00)

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A: As per the instruction, we will be answering the first question. The graph of y=1-cossinx3-1x3-1.

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A: We can find the function g(x) from the given composite function in the below steps.

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A: we already have f'(x)=-sinx-3sec²x so,f'(4) =-sin(4) -3sec2(4)

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A: Given data:- The given points of line is, 3, -2 and 1, 6

Q: (Question-Solution-Final Answer-Conclusion format) B. Generate differential equation by elimination…

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Q: Let f(x)=−3e^x+2+e^4 f′(0)=

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A: see below the answer and calculation

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Q: Give the implicit solution of y'my-x³-2 Oe-2x = y²(x²+c) Oe²-y²-c 2x Oe² = x²(x²-c) 0²¹-y²(x²-c)

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Q: Use the formula for nCr to evaluate the expression 7C7.

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A: Given that a limit problem and we solve this problem by using general property of limit.   Here i…