2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y = a, using two methods. Consider the smaller segment as the area under consideration.

Q: Prob. 4 (a) (6 pciats) If h(x) = (1 + f(x))³, where f(1) = −2 and ƒ'(1) = 3, find h'(1).

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A: This question is related to intersection of graphs, we will solve it using given information.

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A: As per our guidelines we only solve three sub parts of given question and rest of the sub parts of…

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A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

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A: Given, y = x-4(x-3)(x-1)

Q: lim x 1 lim -x 1-x

A: topic:- calculus

Q: 8 i) 이름을 . dx ii) f xel+x2 dx

A: This question can be solved using the concept of definite integrals.

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A: Let's find function is differential or not.

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Q: Prob. 6 (a) 3) Find the critical numbers of the function y = x³/2 - 4x¹/2 3

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Q: ) . Is the differential equation linear? dy dt + y4 = x

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Q: 30. A toy missile is fired straight up into the air having a height of h(t) = 45t-15f² metres after…

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Q: Consider the following function and point. f(x) = f'(x) = (a) Find the derivative of the function.…

A: We need to fill in the blanks.

Q: maximum

A: if you specifically asking to how to find maximum and minimum value. Please refer to the image below…

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Q: (a) AB X AC (b) the volume of the parallelepiped determined by AB, AC and AD

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A: Let's solve.

Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: (1) ਤ + x2 x2 + 3 dx (2) In 2 -e ex 1+e dx x +7 (3) --x-6 dx

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Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: 55. Find the area bounded by r = 4 sin 20 a. a. 4n square units b. 8n square units C d. 4 square…

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Q: Please answer completely. Step by step. Evaluate. S arccos x dx

A: I have stated the used formulas in the solution

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A: Given, u(x, t) = f (x + ct) + g (x – ct)

Q: LORAN (long distance radio navigation) for aircraft and ships uses synchronized pulses transmitted…

A: answer is in next step , i can only answer one question as per guidelines.

Q: 4. The height h in centimeters of Shuntaro's pogo stick from the ground as he jumps on it since s…

A: We have to find the height at given times.

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Q: Evaluate (₁ F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to…

A: NOTE: Refresh your page if you can't see any equations. . C:=smooth curve form (-5,4) to (3,2)…

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Q: II YOLUMES OF REVOLUTION 1. Find the volume generated by revolving about x-1, the area bounded by y…

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Q: Let A(x) = =f(1) dt for f(x) in the following figure. 3 1 y = f(x) +2 3 4

A: The given problem is solved below in detail. The last part as requested is solved in detail.

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Q: Evaluate ln(e2)   a. 2.712828   b. (2.71828)2   c. 2   d. 5.437

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Q: Consider the vector-field F = (2 — ysinr − 1) + (cos x − y ). – - (a) Show that this vector-field is…

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Q: Find the equation of the curve whose slope at any point X-2 3-y and passes through (-1, 1

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Q: Use the Ratio Test to determine whether the series convergent or divergent. Σ n=1 Identify an…

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