Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O Il only Neither I nor II. I and II

Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 - x from above inside x = y2,x = 4.

A: Answer is in step 2.

Q: Find the Taylor series generated by f at x = a. f(x) =x-2x+5, a = 2 The Taylor series generated by f…

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Q: (b) / Vx² – 4 dx

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Q: (NAS 2) Find the directional derivative of f(x, y, 2) = 2 + y + 4.xz at the point (1,-2, 2) in the…

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Q: given below, evaluate lim f(x) and lim x→-00 f(x) = -4x² + 2x +4 sin (9x) ses without bound, you…

A: We have to find the following conditions according to the given information

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is…

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Evaluate the integral: (3si + 9s²j + 4k) ds

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Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

A: Here, the volume formula is given by: V=∫012πy(g(y))dy=2π∫01y13y-13y2dy

Q: 02) Solve the D.E dy - (2x/1-y2)dx 0

A: The given differential equation is dy-2x1-y2dx=0

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of, does the curve has…

A: Given

Q: Let a = ci + jand b = 16i + 12j. Find c so that the angle between a and b is Round your answers to…

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Q: Simplify completely 4 Int dt using FTC-1. da e3z

A: This question can be solved using the concept of Fundamental Theorem of Calculus Part 1.

Q: 3 5 8x 15 dx 5 x4 |

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Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: Find the value of dt Oa 40 Ob.53 Oc 23 Od.13

A: ∫0∞e-3tdt∫e-3tdtSubstitute u=-3t→dudt=-3→dt=-13du=-13∫euduWe know that ∫axdx=axln(a)=eu

Q: 1 lim X0-x23

A: Given,limx→ 0-1x23We know that,For x approaching 0 from the left, x&lt;0  ⇒   x23&lt;0The…

Q: Determine if the given series is convergent or divergent. 3" en – 2" n=1 2.

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Q: Q3) Evaluate triple integral f , (x2 -y²)dz dx dy.

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Q: Remember, even if you enter an answer rounded to a set number of decimal places, if you use that…

A: Law of sines : sin Aa = sin Bb = sin Cc Given  ∠A=38.8°,  a=182.4,  b=248.6

Q: Find the area of the triangle with vertices P(1,2, –5), Q(0,0,0) and R(2, 4, 1). NOTE: Enter the…

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Q: Find f"(1) if Ax) = X+1. %3D 1 1 1/4 12 OOO

A: To find f'1 if fx=xx+1.

Q: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y V9x² + 16

A: The given integral is y=∫dx9x2+16 We have to solve the integral using Trigonometric substitutions…

Q: 3. Given r = t – 1 and y = t-2t, Eliminate the parameter and write an equation in rectangular…

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Q: (-1)" x2n+1 En=0 (2n+1)! Given: sin x = for x ER Determine the exact value of the sum Σ (-1)"(2n +…

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Q: Classify all the critical point(s) of f(x, y) = e(+). Find maximum and minimum value(s) of f(x, y).

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Q: Q2) Solve the D.E dy + (xy – xy²)dx = 0

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Q: Question For the function given below, which statements concerning Rolle's theorem are true? 4x + 3…

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Q: Question 1 Which of the following is the Taylor series expansion of the function 'f (x) =e¬x² with…

A: Given problem:-

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: Find the AuRtaYe value of f(x) = x* on the intervai 2,67

A: answer is in next step

Q: Consider the following function. f"(x) = 48x Find f'(x). (Use C for the constant of the first…

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = for f(x) = cos(x). %3D T2(x) must…

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Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: Q3) Find the Area bounded by the curves x and x = 2y – y².

A: Topic = Area Area bounded by curves is 13.

Q: -6x-'dx

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Q: PART II. Find the derivatives of the following expression, solution must be presented. 1. x²y – ỹ =…

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Q: Find the average value of the function f(x)=e" on the interval (0,4) Da 3725 Ob 490 OC 745 Od 186 25

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Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 =&gt; (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: ind the point of intersection (xo, yo, zo) of the lines given as: L: x = 2 + t, y= 4+5t, z = 5 +t L:…

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Q: Q3) Evaluate triple integral N S dz dx dy. x-y

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows: