Define the function (In(r+ 1)] cosh r+ tan r ,r20 f(r) = (sinh r) sec (r - 2) 0 >r 1. Show that f is continuous at r = 0. 2. Is f differentiable at r 0? Justify your answer.

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A: Let's find. 

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A: By parts method: ∫u(x)v(x)dx=u(x)∫v(x)dx-∫dudx*∫v(x)dxdx ddx(arc(sinx))=11-x2

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A: This question can be solved using sum rule,product rule and chain rule of derivatives.

Q: 1. Determine if g is differentiable at r 0 if 2 cos r, if -1<r <0 9(r) = if r20. r+cos r

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A: Parallel lines

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A: This question is related to definite integration, we will solve it solve it using given information....

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Q: Consider the points A(3, –3, 5), B(5, –5, 2), C'(-1, –4, 2), and D(4, 1, –8). (a) Find the volume of...

A: AB→=(5, -5, 2)-(3, -3, 5)AB→=(2, -2, -3)AC→=(-1, -4, 2)-(3, -3, 5)AC→=(-4, -1, -3)AD→=(4, 1, -8)-(3,...

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A: This question can be solved using the concept of types of sequence.

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A: Let's find. 

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A: Solution is given below:

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A: We have to write about best approximation method

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A: topic - area of parallelogram using vectors

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Q: 3x-28х+49 Зx-7х a. Simplify : i) ii) /x'y . /xy. Write the answer in radical form. b. Solve the equa...

A: i)=3x2-28x+493x2-7x=3x2-7x-21x+493x2-7x=(x-7)(3x-7)3x2-7x=(x-7)(3x-7)x(3x-7)=x-7xor=1-7x

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Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h  by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 - 9...

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A: "Since you have asked multiple question, we will solve the first question for you. If you want any s...

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A: Newton's method also known as Newton-Raphson method is an iterative process that can approximate sol...