Consider the solid region E inside the sphere x² + y² + z² = 4 and outside the cylinder x² + y² = 1. Which region represents the cross section in the yz-plane? (A) (B) (C) (D) V O (D) O (C) O (B) O (A)

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A: Here we use the concept of derivatives

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A: Here we have to use the product rule, quotient rule and general power rule.

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A: We can solve this as follows:

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A: From the property of the odd function we observe that function is symmetric property.

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A: Solution is here

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Q: 7) Find the area of the region enclosed by the cardioid r² = 4 cos 20.

A: To find the area of the region enclosed by the cardioid r2=4 cos 2θ.

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A: Follow the procedure given below.

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A: SOLUTION-

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A: Given :f(x)=2x+3cosx2-2

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A: Follow the procedure given below.

Q: What is f 5√xdx? 3 f 5√√xdx = 5x² + C 2 3 f5√xdx = 10x² + C 3 f5√xdx = 5x² + C 3 [ 5vxdx= 5x? +C

A: Let's solve given integral.

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A: A detailed solution is given below.

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A: Here is the solution:

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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A: This question is based on continuity of function.

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Q: 10. S sinh rai tanhxainhr-tenha -dx

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A: To evaluate: limx→0 cosxx Let y= limx→0 cosxx ⇒y= limx→0 cosx1x

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A: The given equation of the linex2=y=2-z-3which can be written asx-02=y-01=z-23.The given point is…

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Q: Let A be a 2 x 3 matrix, B be a 2 x 3 and C be a 2 x 1 matrix. Which of the following could be ABC?…

A: follow next step

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

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A: Here we have to use the concept of integration

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