dz 10. Compute az and for the following equation. dy e Y + xz? 6xy*z3

Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O V...

A: topic - shortest distance between point and sphere

Q: s(x) = X-4 Find the x-values (if any) at which the function is not continuous. Which of x2-2x-8 the ...

A:

Q: 4x3 %3D 1. mtegrate. de - aya dx 4x3 du = 4x° dx %3D Jxt -2 xp: こ -112 du te 2(x*- 2) ° +C %3D %3D

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Q: Use Stokes' Theorem to calculate the integral | F. dr where F = (y – x)i+ (z – y)3+ (x – 2)k and C i...

A: Solving the following integral problem

Q: 15. Find dr/d0: r = 4 – 02 sin 0 а. 20 sin @ - ө2 cos @ b. 0 cos e – 0² sin e - c. O sin e – 02 cos ...

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Q: Evaluate the integral of the improper fraction using partial fraction method - 2x + 6 + 1 d. 2x-8

A: We have to find given indefinite Integration.

Q: Given the Table of Values for the given limit, which of the following is FALSE?

A: The objective is to find the false option.

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

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Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx ta...

A: On solving this we will get

Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

A:

Q: a. The graph of a monomial function f is shown below. 25 20 15 10- 5 -5 -4 -3 -5 -10 -15 -20 -25 Com...

A: Please see the below picture for detailed solution. 

Q: The revenue function Rin terms of the number of units sold, a, is given as R= 250z – 0.32? where Ris...

A: topic - functions and application of derivatives

Q: Homogeneous Equations [x csc() – y] dx + xdy = 0 O In = cos() In/cos(;)| = = CX

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Q: Example Find the domain and range of the following functions : x +7 if - 35x<5 [2-x if 0 <x<2 x - 1 ...

A: (i) f(x)=2-xif 0&lt;x&lt;2x-1if  3≤x&lt;4(ii) f(x)=x+7 if  -3≤x&lt;5x2if   5≤x&lt;76-2xif   x≥7

Q: What is the maximum value of f(x) = x³ + 3x2 -2 ? %3D Answer:

A: Solution: f(x)=x3+3x2-2 find the maximum f(x)  

Q: e2t+a (2 cos at – 3 cosh 2at) -

A: We have to find Laplace transformation. 

Q: 1- 2x b) f(г) — x² + 1

A: (b) To find the derivative of  f(x)=1-2xx2+1 The function is of the form f(x)=uv where u and v are f...

Q: 8. Detemine the area of the region enclosed by the curve y = x +4 and y = x+4. %3D

A: The given curves y=x2+4 and y=x+4  

Q: 1 dx Evaluate -1 x2 O 2 O -2 O O

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Q: Given: x² dx Find: Formula 1 o fe'du

A: Given problem:-

Q: Evaluate the integral tan 4x S- Vtan? 4x – 24 In/tan 4x + /tan² 4x – 24| +C O 1 sec 4x +C Arcsec 5 O...

A:     14lntan4x+tan24x-24+C' =14lntan4x+tan24x-24' +C' =sec24xtan24x-24+0=sec24xtan24x-24 So, the firs...

Q: Evaluate the integral S/5+12x² – 4xª xdx (5+ 12x2 - 4x9) +C (2x2 - 3)W5+12x? - 4xª + 14Arcsin - 4xª)...

A: We can evalaute the integration as follows:-

Q: The sum of one number and three times the second number is 48. What will be the maximum product of t...

A:

Q: 25. f(x) = 1 – V

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: Find the derivative of the given. f(x)= cos x cot x let g= cos x and h= cot x. Then, g'= -sin x an...

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Q: as x approaches 0 using the table of values? II. -2 -1.5 -1.1 |-1.01 -1.001

A: We have to choose the correct option according to the given information using the definition of limi...

Q: 6. Find the derivatives of the following functions/curves: a) sin(y?) + cos(x²) = xy 1 — 2х | b) f(г...

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Q: Prove that lim X-2 2x2-3x-2 = 5. x-2

A: Topic = Limits

Q: dx Evaluate -1 x2 - 0 -2

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Q: What values of x make 3(x – 5)(x – 12)(x + 5) = 0? If there is more than one answer, enter your answ...

A: Topic = Algebra

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: The length of string is 48 cm.Let the length of the one piece is x,Suppose, equilateral triangle wit...

Q: 2.1x + 11.1 if r – 1 if z = – 1 Determine which one of the following rules for continuity is violat...

A: Given query is to find the rule whic is violated.

Q: Consider the following graph. y 3 2 1 X -10 -8 -6 -4 -2 2 Identify the parent function represented b...

A: The objective is to identify the parent function ,the transformation represented by the graph and th...

Q: 3 sin? 4t + 8 cos² t

A: Solution: L{3sin24t + 8cos2t} Use the following identity : sin2x=12-cos(2x)12 =L{312-cos(2·4t)12+8co...

Q: Find F. dr, where F = 3yi – 8x3+ (8y – 8x)k and C is a - circle of radius 8 in the plane x + y + z =...

A:

Q: 7. Absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4

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Q: Use sigma notation to write the Taylor series about x = xo for the function. e; xo = 10 O 00 e10 E* ...

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Q: ue Theorem on the given interval? ction satisfies the Mean Value Theorem. continuous on [0, 3] and d...

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Q: Solve the differential equation with appropriate method. Simplify final answer free of fractions and...

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Q: Exact Equations (w³ + wz² – z) dw + (z³ + w²z – w) dz = 0 O (w² + z?)² = 4wz + c O (w? + 2?) = (4wz ...

A:

Q: Use sigma notation to write the Maclaurin's series for the function f(x) = x cosx. Show complete sol...

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Q: 4x4 + 7x + 16 Consider the rational function f(x) 6x2 – 11 a. What monomial expression best estimate...

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Q: Vx sin/x Find: Formula 0 2 fsin u du 2 | sin u du | sin u du Sesc u du

A: We have to choose the correct option according to the given options

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2...

A: We will use the fact that  The Mean Value Theorem states that if a function f is continuous on the c...

Q: 1. How many terms are there in an arithmetic sequence with first term 10, common difference of 2, an...

A: Note: As per our company's guidelines we are supposed to answer the first question only. Kindly ask ...

Q: What is the reversed order of integration of dydx ?

A:

Q: Evaluate the integral dx 2x3 - 3x x |/3x - /2 2/2"V3x + v2 1 +C O 16V2 + V3 In 3 |/2 - 3x +C In +C 2...

A:

Q: Suppose that f(x, y) = 5x + 2y on the domain = {(x, y) | 1 < æ < 2, a² < y < 4}. D D Then the double...

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Q: V9 – x2 Consider the function f(x) = 3 Let R be the region bounded by the curves y = f(x) and y = 0 ...

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

A: We will use the following concepts:-