Show that the set {e^n: n ∈Z} is countable. (Hint: Use the function f (n) = e^n and show it is 1-1 and onto).

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: dx Evaluate f- +1) using the Cauchy principal value.

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Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

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A: The given function is: x,y=1 if x=y0 if x≠y

Q: 19. The 68-95-99.7 Rule. A set of test scores is normally distributed with a mean of 100 and a…

A: Note: As per instruction solving D-FGiven information,population mean = = 100Population standard…

Q: Prove for a > 0:

A: Integration of the function helps to prove the required identity. A number can be written as the…

Q: Show that /I +x 0.

A: Mean value theorem: Let f be a function satisfying the following properties: 1. f is continuous on…

Q: -1 if x 2.

A: We see, the points at which the function g(x) has split definition, i.e., at x = 0, 2, g(x) can be…

Q: Verify the rule by differentiating. Let a > 0.

A: the given rule is: ∫duuu2-a2=1aarcsecua+C where C is constant of integration.

Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: Use a formula to express w as a function of t if w - V4s + 5 and s- ef - 1.

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Q: Use quotient rule to show that /dx(cscx)--cscx coty Show AU Wonc

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Q: lee f: R>R be a C function ミく。 proper tg with 2f show that F is cunservative

A: Please check step 2 for the solution.!

Q: Let f=​{(0​,8​),(5​,0​),(9​,4​)}. Find f(0)

A: We have given f.  We have to find f(0)

Q: f(x,y)=x² + 3y + 7. R is he region shown in Fig. 5 (include the boundary). y =2-x y-4- R Fig. 5

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Q: 4- 13 + 6y = 0 dx

A: We have to be find

Q: Write an expression for the linearization of f at a

A: Given:Linearization of  f at a

Q: The domain and the rang of the - * function In (x - 2) are

A: the log function is not defined for zero and negative numbers so the value of x-1 should be greater…

Q: Let f = {(1, 2), (3, 4), (2, 6), (5, 9}. Find the domain of f

A: Given function  f = { ( 1 , 2 ) , ( 3 , 4 ) , ( 2 , 6 ) , ( 5 , 9 ) }

Q: %31 -I(x) Prove that Bassel function

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Q: Find the rule for (f ogoh)(x).

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Q: Suppose that o f (x) dx = 3. Find L f(x) dx if, %3D

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Q: Consider the triple integral ffw xyz2 dV, where W is the region bounded by z = 36-y², z = 0, Write…

A: Given triple integral,where W is the region bounded by  We have to find the x bounds.

Q: f (x,y)= y² -2x² +10. Ris the region bounded by the parabola y = x and the line y = 4.

A: According to the given information, it is required to find the maximum and minimum value of f on the…

Q: = Let p¹²-2x+1, p² = 3 +3x+1 and p35x + 10. Let = x³-3x + 4. Is q in me span of pl,p2 and p3?

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Q: Let x > 0 and b > 0. Show that

A: