The volume of the solid region, in the first octant, that lies below below the surface, z = above the plane z = 0 and inside the cylinder, x² + y = 9, 9n is equal to Select one: True False

Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: Find the standard form for the TANGENT PLANE to the surface: : = f (x,y) = x cos (xy) at the point…

A: The given function is  z = f(x,y) =x cos(xy)

Q: Evaluate the defınite integral. e? i +ej+t k)dt e? i + (e- - 1) j+1 k 7 e? - 1 i - (e- - 1) j+ 1 k 7…

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Q: Find the general solution of the given ODE x +1 y': y* +1 x? + r- - y? = x +4x + k Option 1 O Option…

A: integration

Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: Find the area of the specified region. 5) Inside the limacon r= 8 + 2 sin 0

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Q: Compute the area bounded by the cardioid r(0) =1– sin(0) on 0, Express your answer as a decimal…

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Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows

Q: 1. Which of the following integration techniques should be used to evaluate f. sec? x V4 - tan? x}…

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Q: L x² cos 2x³ dx? After substitution is performed, which of the following is equivalent to

A: Given that the integrals  To find the evaluate and choose the correct answer

Q: Find the length of the curve 7(t) = (4t, In(t), 4t²) for 1 <t< 4 Add Work Submit Question

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Q: Suppose we have the position function: r (t) = t. t2 Evaluate the tangential component of…

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Q: Perform the following operations and express the results in rectangular form: a. (8.21+j4.31) –…

A: Rectangular form

Q: 4. A cherry pie with a temperature of 120°C was placed on a table to cool in a room of constant…

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Q: 2 2 2 2 4' 16' 64' 256' 1024

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Q: A ladder 42 feet in length rests against a vertical wall of 36 feet in height. What is the measure…

A: Given query is to find the angle of elevation.

Q: 1 is convergent or 8. 1) Use the Comparison Test to determine whether the series n=2 divergent. Show…

A: We need to find if series is convergent or divergent,

Q: P5: |V4- 9x?dx 4 –

A: Let's find.

Q: dy into 11. The rationalizing substitution y = u° transforms J 7(1+ В. 6 f и du D. 6J TFu² du С. 6 /…

A: Given problem:-

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: The value x = a is a critical number for f (x). Classify a as a local maximum, cal minimum or…

A: Given f(x) = x^3 -12x^2 Also given x=8 is critical point  now we have check at x=8 has maxima or…

Q: P7: x3 + x – 1 x(x – 1)(x + 5)²

A: The given problem is solved below in detail.

Q: 8. The rationalizing substitutionw + 4 = u² transforms - dw into w+4 A. fu² - 4°du B. 2fu² - 4}du C.…

A: Given: I=∫w2w+4dw  ...1   As we know that; The Power law: ddxxn=nxn-1 And ∫a·fxdx=a·∫fxdx , where a…

Q: (a) Explain why the function f(x) = e is not injective (one-to-one) on its natural domain. (b) Find…

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Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: Use the Comparison Test to determine whether the series > is convergent In -1 n=2 divergent. Show…

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Q: Give your answer correct to Use differential to estimate the value of y 4.01 V4.01 8. four decimal…

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Q: f(x)=/1+2sin x j. f(x)=e" +4* +sinh(10x)

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Q: 1 dx x(x3000+1)

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Q: A cube 3 inches on an edge is given a protective coating 0.1 inch thick. About how much coating…

A: solution:-edge of cube=3 inchescoating=0.1total edge length of cube with coating=3+20.1=3.2…

Q: The Mean Value Theorem states: For any function, f, differentiable on (a, b) and continuous on [a,…

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Q: 26 State the Fundamental Theorem of Calculus . you must state the first and the second fundamental…

A: On solving this we will get

Q: y y = x² + 1 5. y = x 2.

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Q: EXAMPLE 1: Consider the graph of the function f given below. Using the given graph, determine if the…

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Q: a. 0 =-45 → graph type = b. r= 8-8cos0 graph type = facing up/down/left/right? loop length = c. r=…

A: (a) θ=-45°Graph type straight linesymmetry along first and third quadrant     (b) r=8-8cosθgraph…

Q: 12. Which of the following is equal to dx upon decomposition? х3 — x2 -2х 1. 6 A. C. 2+ х - 2 dx x…

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Q: 1. For the curve x2y2 = 25 at (-1,-5), find the equation of the normal line.

A: The given curve is: x2y2=25 Differentiating it with respect to x: y22x+x22ydydx=0 at (-1,-5):…

Q: f4) = (/4x² +8 - x²)* (8x + 4x)V4x2 + 8 - 24x - 32x V4x2 +8 If then f'(x) =

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Q: Find curl (4z i + 5x j+ 3y k).

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: Find the limit, If it exists. x- 1 lim X---

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Q: Which of the following equations is a homogenous DE? O (xy? + x)dx + (x²y- y)dy=D0 O (x- y)dx+ (3x+…

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Q: 1) Use the Integral Test to determine whether the series > 1 is convergent or divergent. n=1 (3n–…

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Q: y = xx, x 4, and y = 0 Revolve the area of the shaded region about the x-axis. Using circular disk…

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Q: 9. Verify the identity 1 1 = 2 sec² x 1-sinx 1+sin x

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Q: EXAMPLE 1: Consider the graph of the funetion f given below. Using the given graph, determine if the…

A: topic- continuity of a function

Q: Find V. (V x F) if F(x, y, z) = 4 sin xi + 5 cos(9x – 10y)j+ 10zk. V·(V × F) =

A: topic- vector field

Q: Find the area between the curves f(x) = x2+2x+1 and g(x) = x+1

A: We need to find area between given curves.