Let f be of the class C" in the interval [a.b] and let c be an interior point of this interval with f'(c) = 0. Then if f"(c) <0 then f has a local maximum at X = C

Q: (b) Find the singular solution of дz where p = and q ax = z = px +qy+p² +q² + pq, дz ду

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Q: Q2(a) The temperature at one end of a bar 10cm long and with insulated sides is kept at 0°C and that…

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Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

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Q: 2. Solving the equation t A) f(t) = 1+ est 1 B) f(t) 1+ est t C) f(t) 1- est D) f(t) 1 - est [₁ f(u)…

A: Solution :  Options (B) is correct

Q: 4. Solve the following 2nd-order OPES (5 Steps) day - (22) + (4-1) dy dx² Y(0) = 4 , y(0) = 1 y cas…

A: We can solve this using euler method of second order differential equation

Q: 7. Alan has 20 ducks and goats on his backyard. The animals have 64 legs altogether, how many ducks…

A: Alan has 20 ducks and goats on his backyard. Animals have 64 legs altogether. We have to find the…

Q: 5. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: please comment if you need any clarification. If you find my answer useful put thumbs up. Thank you.…

Q: sing cylindric -2²2², 0≤ solid B that 2 = 2 using s

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: Set up the triple integral that will give the following: the volume of the solid B that lies above…

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Q: 2. A man put a pair of rabbits in a cage. During the first month the rabbits produced no offspring…

A: According to the given information, a pair of rabbits produced no off springs in first month but…

Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

A: Given, Time for placing bacteria is 8 A.M. Every hour, the area covered by the bacteria is doubles.…

Q: Consider the region bounded by y = x², y = = 2x Write, but do not evaluate, an integral to find the…

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Q: 3 By direct partial integration, Solve the following PDES 8- X²Z ахду 4 JZ = 0, Z(X₂0) = x² + x, Z…

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Q: Consider the integral: f(t)-10e-15t = 17t- -S sen(t-u)f(u)du When applying Laplace transform in both…

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Q: Let Xis Hilber @ 1| + |1

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Q: Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but…

A: Given that Ronnie goes to the racetrack with his buddies on a weekly basis.

Q: An internet job recruitment company, Company1, claims on their company doubles the probability of…

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Q: The region bounded by the curves y = r² and y = x³ is rotated around a. the z-axis; b. the y-axis;…

A: the region bounded by the curves y=x2 and y=x3 is rotated around  a) the x-axis b) the y-axis c) the…

Q: A study examining the relationship between pre-diagnosis physical activity and cancer enrolled a…

A: Given: A study examining the relationship between pre-diagnosis physical activity and cancer…

Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: What is the negation of the proposition/statement: 9 14                                  b) 9 ≥ 14…

A: Solution :  Options (B) is correct

Q: (5 6 By Separation of variables, Solve the following PDES :- ²4 24 . 84² dx² 0 o u(e,t) = u(s, t) =6…

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

A: Conditional probability  If two events A and B associated with a random experiment . Then the…

Q: Does the following series converge or diverge? Σ 4√n 10n3/2 +7n+7 n=1 The series diverges. The…

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Q: show that ф (x, y, z) = 8²4 PDE: аф дуг дуг + + даф x². 2 +у2 + Z2 =0 872 satisfies the

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Q: Find the differential dz of the function f(x, y) = 4y²+x²y-2xy and use it to approximate Az at point…

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Q: Q2: If P(A) = 0.25, P (B)=0.45, P (AB)=0.43, draw the Venn diagrams and determine the following…

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Q: Solve the following differential equations by linear method. dy dx + 2xy = 0

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Q: Find the general Solution of the following PDES -X • 3 их + 2 Иу U (x₂0) = 4x 2 e (3y-2x)/2 ans-…

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Q: Give example of projection in Functional Analysis

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Q: Q1(a) A function y = f(x) is given by the following table of values. Make a harmonic analysis of the…

A: Given table, x 0 1 2 3 4 5 6 y 4 8 15 7 6 2 4   As we Know…

Q: 55² +25-4 (S+₁) (S+2) (S+ 3) Taking Laplace transform

A: The given expression is                5s2+2s-4(s+1)(s+2)(s+3) First we shall write the given…

Q: 4. Evaluate the double integral: Sa+1 ¹/3 27 +1 (Hint: Change the order of integration to dy dr.) dr…

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: Use the following information to answer the next que An internet job recruitment company, Company1,…

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Q: 19. f(x, y, z) = x² + y² + 2², holds 2x + y + z = 1, -x + 2y3z = 4

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Q: Q3: Use Euler's Method to find a numerical solution of the differential equation dy y = 3 - dx X =…

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Q: Let a₁ = a₁ = a₂ = 2 and an = an-1 + an-2 + an-3 for n > 3. Prove, using strong ao mathematical…

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Q: Given that A = (¹ 1) •[1]. and -1-eigenvector equal to 2 -1 +628968 A = has eigenvalues -1 and 3…

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Q: Q1. Find the point of intersection of the lines L, and Ly whose equations are given as: L₁: (x = 1,…

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Q: x1 + 5x₂ + 3x3 = 30 3x1 + 7x2 + 13x3 = = 80 12x1 + 3x25x3 2 (0) (0) with ¹ [x(0), xQ), xº)] = [1, 2,…

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Q: Q4\ Find the average value of f(x,y) = (+√y) where 0≤x≤y and 0 ≤ y ≤ 4.

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Q: the area bounded by the parabola y ² =4ax, the y-axis, and the line y=2a revolves about the line…

A: given that the region is bounded byy2=4ax and y=2a and  revolves about y=2a Graphically,

Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: By direct partial integration, Solve the following PDES 8- • Xd²z ахду dz ду + =0 Z(X,0) = X+X =X+X,…

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Q: Evaluate the double integral: LLantes x² +1 yl/3 (Hint: Change the order of integration to dy dr.)…

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Q: Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but…

A: We will start with a variable and then follow sequence of event to get value of the variable

Q: 6. A rectangular classroom has length that is 1 meter more than 2 times the width. Find the…

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Q: 1. 5) The differential equation dy 2 d²y x² dx² 7x- +16y=0 da has x4 as a solution. Applying…

A: We are given second order linear homogeneous differential equation with variable coefficients which…