The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) = (0,0), (c) {(x,y) = (0,0)} (d) None if: (x, y) = (0,0), is continuous for the set.

Q: f(x, y) = x² - y² + 10x +12y - 64 −x² −

A: To determine the extrema if any for the given function.fx, y=-x2-y2+10x+12y-64

Q: -2 Evaluate: ²₁5²[(x²-²²] | du dt x+y

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Q: S f(x) dx = [ -6 -5 f -2 Y 7 3 -3 7 X

A: This above given expression of integral is shows integral value of function f(x) from x=3 to x=7.

Q: Find a potential function f for the field F. F = (5y + 2z)i + (5x + 3z)j + (2x + 3y)k A general…

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Q: let f(x)=x +9x-1 if (f o g)(x)=x+9√x-1. find g(x)

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Q: The value of A. +3+2x² +C C. = + x² +2+C 20 [ (² + 3) *²x² dx B. +³²+3x³ + C 28 D. none of the…

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Q: 2+x a) lim x-22+x²

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Q: A- Answer the following L-1 3s-1 s²+2s+5

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Q: When solving ff(u)du = t - e³u f(u)du you obtain 1 A) f(t) 1-e³t t B) f(t) 1+e³t t C) f(t) 1-e³t 1…

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Q: t√√t + ,2 + t dx

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Q: 1. Simplify. Write "undefined" for expressions that are undefined. 1 -6 030-0 [B]- 4 + 5 -2 4.)

A: To simplify.

Q: find the Fourier series of half rang periodic function. f(x) = x|x| -π < x < π <x<π

A: We know the following. Fourier series of function fx on interval -L≤ x≤ L is defined as:…

Q: 2. Express the iterated integral as a double integral in polar coordinates. 1 X 1 Lo dy dx 16/2 x² +…

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Q: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: The value of √x dx 1+ A. x-2√x+2 ln (1+√√x) + C B. x-2√x-2 ln (1 + √√x) + C C. x-2√x+2 ln (1+√√x) -…

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Q: Evaluate: 1+ 2y dy dx •x x2

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Q: Differentiate the function with respect to y. A Z = + Bey уб Z' + Bey = 8A 9 y 20 -

A: In this question we have to differentiate the function with respect to y.

Q: 8. The value of ve A. sin-1 (e) + C C. sin-1 (e-x) + C dx B. -sin-1 (e-2x) + C D. sin-1 (e-2x) + C

A: Topic = Integration Correct option = A

Q: = Find the area of the region bounded by x = and the y-axis using the horizontal strip. 4 2y²+1

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Q: S- tanh e cosh(z) – sinh(z) -dz

A: Let's evaluate given integral.

Q: 4. Evaluate the double integral that will find the volume of a solid inside the paraboloid z = 1 -…

A: We need to find volume.

Q: зи Evaluate the integral: So So So u s2 +u2 ds du dt

A: Given: I=∫02∫0t∫03uus2+u2dsdudt   As we know the common integral. ∫11+x2dx=tan-1x+C

Q: San 4h (x) dx = [ -3 y h 8 2 AN -3 10 4 -1/ -7 -7 7 x

A: From the graph, note that: ∫-30h(x) dx=-1 because area bounded by the curve h(x) is -1 in -3 to 0.

Q: 3 .4 ²³₁₂₁ (4x²y — z³) dz dy dx

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Q: Prove the following using the principle of mathematical induction. For n > 1, 1 1 1 1 = + + + 54 ( –…

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Q: 1. Find the angle between two vectors a and b with magnitudes √3 and 2, respectively having a b =…

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Q: valuate: xy² dx dy

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Q: In 3 2 – sinh x tanh x cosh x dx

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Q: 4 Verify that the Mean Value Theorem can be applied to the function f(x) = x 5 on the interval [0,…

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Q: 4 Find the area of the region bounded by x = 2y²+1 and the y-axis using the horizontal strip.

A: Let's find area of region bounded by given curve and y axis.

Q: Find the area of the region bounded by the curves 1 y = (x+4)²¹ Y = 4 and the x-axis using vertical…

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Q: Given f(x)=x²-1 on [-2,2]. a. Find the critical numbers of f on the given interval. b. Determine the…

A: A critical number of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Find the particular solution of the DE y11 + 24y = 0 subject to the initial conditions y(0) = 2 and…

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Q: swers: i i Mi 0 0 O

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Q: (3) If R is an integral domain has non zero characteristic, then Char(R)=..... (i) 5 (ii) 4 (iii)9

A: This is a problem related to function and number system of the function. Based on the general…

Q: II. Find the inverse of each matrix. 5 -11 1. -7 -9

A: This is a problem related to matrix. Based on the general formula and concept we will find out the…

Q: = 10. Find a second-degree polynomial P such that P(1) = 7, P'(1) = 7, and P"(1) P(x) = Need Help?…

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Q: 1. The simple interest charged on a 60-day loan of Php 8,400.00 is Php 119. Find the simple interest…

A: Use simple interest formula

Q: Find the area of the region enclosed by the curves y = 4 24 8 0 16 x³ and y = 4x.

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Q: Find the area of the region enclosed by the curves y = 4 24 8 16 O O x³ and y = 4x.

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

A: (1) we have to fill in the blanks Let I be a proper ideal of the commutative ring r with identity.…

Q: Find the solution of the given initial value problem. v- 7 y = y' cost t-7' y (π) = 0, t> 0 y(t) = =

A: The standard form of the first-order differential equation is: dydt+Py=Q Where P and Q is the…

Q: show that V(x, y) = x 'f (2x+y) is the genera Solution of : du 2X x av ах 1 ду

A: First, we find ∂v/∂x and ∂v/∂y  and substitute them in the given equation, if it satisfies the…

Q: The value of A. sin-¹ x +√1+ x² + C B. sin ¹x-√√1 + x² + C C. sin-¹ x + √1- x² + C D. sin¹x-√1- x² +…

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Q: The value of A. +3+2x² +C C = 1 + x² +2+C 20 [ (² + 3) *²x² dx B.+²+3x³ +C D. none of the answers

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Q: The value of A. -√4+C 4x B. +C √4-2 C. D. 4√4-x² 4√4-x² S ₁4- +C +C dx (4- x²)1.5

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Q: True or False? 4. Let f : R → R be a function defined by f(x) = x^2+1. If B = {2, 5}, then…

A: according to the company rule we can answer only the first question and rust can be reposted.

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: To find the volume of the solid that results when the shaded region is revolved about the indicated…

Q: 3 -1 0 2 2 х -у 2 x+y 2 dx dy

A: Given

Q: Q5/ Solve for x the following inequality and show their solution set (x: x2-x-300)

A: