1 5) f(x,y)= x+ y

Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

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Q: If f(x, y) = (17x - y)3, then is given by: af dy (17x (17 – ) 13 - 18 (17x 13 - - 13 Y)2 – ) 18 (17x…

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Q: 5. The function f(x) = (x+ 5)(x- 3) is dilated by x to produce the function g(x) = x f(x). How many…

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Q: 11. Let f(x) = C•b*. Determine constants C and b so that f(-1) = 10 and f(2) ==. А. 1 В. C = 5,b =…

A: Make two Equation By using given conditions and than solve it.

Q: Find the constants m and b in the linear function y = f(x)= mx + b, such that f(1) = -2 and f(3) =…

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Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

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Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

Q: Find if x'y+y' = x dy dx A) 2x+2y 1-2xy-2y B) x2 1-2ху C) x2+2y D) O A O B O c O D

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Q: (a) Find the constants A, B, C, and D that satisfy 1 1 1+ (w/o)² 1 + ((z-w)/7)2 Aw B Cw D 1+ (w/o)²…

A: Use partial fractions

Q: 11. According to a formula discovered by the French physician Poiceulle, the velocity (in cm/sec) of…

A: According to a formula discovered by the French physician Poiceulle,  the velocity (in cm/sec) of…

Q: Y₁' = 3Y₁ + 1/₂ ل3 Y/₂ = 2y + 2y₂

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Q: y = x + C,e* + C,e-2*

A: y=x+C1ex+C2e-2x

Q: 13 |xsin xdx ーT 15 (xsin xdx

A: I=∫ x sinx dxIntegration by parts;u=x, v=sinxI=x∫sinx dx-∫(1 ∫sinx dx) dxI=-x cosx +∫cosx dxI=-xcosx…

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

Q: xy* Let f (x, y) = if (x, y) # (0,0) and f (0,0) = 0. (a4+6y8)

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Q: 3. Show that f(x, y, z) fxx + fyy+fzz = 0. = 1 x² + y² + z² satisfies the equation

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Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: + y = 2. What is y" at the point (1, 1)? y ² Suppose that x +

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Q: 10. Differentiate each function. a) y= -3x² + 4x- 5 b) f(x)=6x-1- 5x-2 ) flx)= 4\x d) y= (3x² –…

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Q: Determine the length of x = 3+ (y – 2)², 4<x< 19

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Q: The function 3 y = -x³ (2x – 3)(4x + 3)° is negative on the intervals ) a) x E (-∞, –) and x 4 X 3 E…

A: The given function is: y=-x3(2x-3)(4x+3)3

Q: 5) The equations r² + y²s + yt² - 13 and y² + x²s + rt² = 9 define s and t as implicit Əs functions…

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Q: dx. = 9) Evaluate 2x-1

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Q: 2. In y = c+ C2*

A: We have to eliminate the arbitrary constants c1 and c2 from the equation lny=c1+c2x. This is…

Q: 2. fote-t² dt

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Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: 12) y- 3x+ 2x

A: We know that ddxxn = n·xn-1

Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

A: Given function is, fx,y=4y2x3+ex2y To find fxy(x,y) Find fxx,y partially differentiating the given…

Q: If B = x°ya, + (2x + y)a, – (y – 2)a, find (a) V B (b) V X B (c) V (V B) (d) V x V X B

A: Given : B=x2yax +(2x2+y)ay - (y-z)az

Q: Q3) a) find f sec³ x dx

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.