Problems 1. Give the order of each of the following PDES Ur + Uyy = 0) b. Uzzz + Uzy + a(x)uy + log u = f(r, y) c. Ugrz + Uzyy + a(x)u=ry +u² = f(x, y) d. a. %3D u Uzz + u + e" = 0 Uz + cuy = d е.

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: 3. logi (x2+x)- log(x+1)=2 А. 2 О А о B О с O D B. 16 с. -8 D. - 16

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Q: 15. If log, b? = 5 determine the value of log, (a²). 16. Solve for x, log , (x-4)+ log,(x+2)=1 and…

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Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: f(mıy)= √(Y+1) ² (n+1) log (n-y)

A: A function is given and we have to find its domain and range. Domain is the all the input values to…

Q: Can you show work for how to get W and L

A: Sure, let's go through the calculations step by step.1. **Given Data**:  - \( d_{max} = 0.009 \)  -…

Q: Vx-5 5. Find for y = In| Hint : Use the properties of the logarithm dx \4x3+1 function before…

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Q: y'= lagg (2x -Ay +5) When gpplym2 the vawable chonge u=2x -4 y+5 the eqn convents ' 'into? %3D O a)…

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Q: а. (у + 2)2— 2x log y - In u = 2e-x, k > 0 ay ax? ду? b. uxx + xy uxy + y²u² = 0 = v2 + x azu C. t-…

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Q: 17. Expand the expression Vx+1(x² - 4) |ninon se log2 183 (r°+27)* -3 081 2

A: Given expression

Q: Use f(x) = ex-3, g(x) = 5 + log x and h(x) = In x to evaluate problems 5-9. Give the approximate…

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Q: Solve the equations given in Problems 17 to 22 17. logr – log = log Sx- log2x 18. log2³ – logt = log…

A: Dear,as per company guidelines we can answer only 3 questions, please post other questions…

Q: 23. Show that by Newton's Law of Cooling, the time required to cool an object from temperature A to…

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Q: 28. If y = 7* , x €R, the inverse function is Oy =log7 Oy =x7 Oy =log,7 %3D Oy =log7æ

A: We have to solve

Q: 3. Suppose i h(x, y) log(3x) Actan (¹) Find h(x, y), hay(x, y), and

A: Solution : z=h(x,y)h(x,y)=log3xtan-1y4 hx(x,y) is partial differential of h with respect to x,…

Q: 7. If log,w= and log; x+logs y=1 , then what is the value of 13 w3D 7 log, +log, 36x y ?

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Q: 2. Expand the following natural logarithms: In(zx'y") b. In- zy а.

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Q: - If you know that log4 x = 2 and log5 x(2y – 1) = 1 calculator 7x + 10y – 1 Between which of the…

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Q: -2 4 x 4x y simplifies to: 48 Number 4 2.

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Q: x* + y* ди ,showthat ди + y- 3 If u(x,y) =log х+у ду

A: For the given  u(x,y) =log(x4+y4x+y)

Q: 3. Which equations are correct? In 2r In 2+3 Inx- Iny = a. Iny b. log 5+ logx +5 logy = log 5xy 9x…

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Q: 36. Given log, 2 = x, log 3 (a) 2x+y+ 2 y, log,5 = z. Find log,60. (c)x+ 2y %3D %3| (e) 2x +y+ 2z…

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Q: 3. Show mathematically for which p1, P2, ...Pn are the following functions attaining their maximum…

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Q: Prove that log(x + y) = log(x) + log(y) if, and only if, y = 1, where x > 1.

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Q: If ƒ (x, y) = log (x² + y²), then f +f, is equal to XX yy 1 (a) x² + y² (b) 0 2 1,² - x² (c) (d) (x²…

A: If f(x,y)=log(x2+y2) Then to find fxx+fyy=? Here we will use the following formulas-…

Q: Find ds ldx if y=3) X(X+1)(x-2) (x² +1) (2x+3)

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: For items 1 - 2, Let f(x) = a 1, where 0 < a # 1. 1. Let Which of the following is the graph of…

A: According to question,Given function,fx = a-x-1

Q: If x = log, 2 and y = log, 4, find log, 15 in terms of x and y. 2x + Y А. 2x+ Y В. y(1+4x) 4x + y C.…

A: Given: x=log92  =log 2log 9  =log 2log 32  =log 22log 3⇒2x=log 2log 3y=log54  =log 4log 5  =log…

Q: 15. If the points (2, 3), (-1, 0), and (-4, -1) are on the function f(x) = a*, what points would be…

A: Function fx=ax Points on the function fx=ax are 2, 3, -1, 0 and -4, -1