Q 2: Fill in the blanks for following Sentences: 1. For any f(x,y,z), f¯ is not conservative if .. .and f→ is incompressible if.... 2. To test the increasing of any function f(x,y) at a point ( xo, yo) we need to know 3. To find the particular solution of the Initial value problem (I.V.P), y" – 4y' + 4 y = e2t , Then Yp

Q: 4. If [æf (x) + 2] dæ = x³ – a² then find the function f (x). 3 A) 2 3 B) 2+ C) 3- 2 E) 2– D) 3+ --…

A: The given equation is x∫x fx+2dx=x3-x2.

Q: 6. If f(x) satisfies 0 < f(x) < x for 1 < x < 3, what is the maximum possible value of the average…

A:

Q: 6. Let A and B be two open subsets of R". Show that their intersection An B is also an open set. 7.…

A:

Q: If f (x) = x² – 4, what is the simplest form of +1), %3D - X -1 Select one: a. х + 3 о ь. х — 1 c. x…

A: The given function is: f(x)=x2-4

Q: Which of the following is equivalent to the function f(x) = 4x2 + 12x-6? A none of the given choices…

A: Solution: f(x)=4x2+12x-6

Q: X 1. Find and draw F, (y) and fy(y) in terms of Fx (x) and fx(x). 2, for x<0 ↑ f(x)

A: From the graph of the given distribution function it is clear that we can say the Y is related as…

Q: The Domain of ƒ(x) = V1- x is

A:

Q: 46. If f(r) = 2ur +|r – 2| – ||| and 0 < z < 2, then S(z) = A 2 B 2+ 4x C 2-4r D -2+ 2x 2 –

A: Given that fx=2x+x-2-x with 0≤x&lt;2. Since 0≤x&lt;2, we have  x-2&lt;0 and  x≥0. Now,…

Q: 10. (a) Find a combination of step functions that is equal to 4 when 2 ≤ t ≤3 and equal to 0…

A:

Q: (1) If x + 0, then +0 and A = x. (2) Let a, b e R. a² + b² = 0 if and only if a = 0 and b = 0. %3D…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: Find x and y for which the following equation is satisfied: x+2 = - 5+i i-5

A:

Q: 14)- Consider the following formula f"(x,) = a-4fo+3f-1 _ 2hfm(C) 6h2 3 Find the optimal h.

A:

Q: 5. Given n constants ki (with i = 1, 2, ..., n) and n functions f(x), deduce from Rules Iv and V…

A:

Q: 9. Which of the following statements is TRUE? A Ifx² = y² , then x = y. B Iff(a) = 0, then x + a is…

A: Here we have to select the correct statement from the given statement.

Q: Only one option can be true

A:

Q: 1.1 Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x;…

A: Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x; y)…

Q: Given n e N and the function f : R" → R", we can define, for each nonnegative integer k, the kth…

A: (f) Given : f : ℝn → ℝn is linear function,  where n∈ℕ. To show :  We have to check whether the…

Q: 10. Let f(z) = 4z7z²+3z +1 and g(z) = 4z7. Show that f(z) - g(z)| < |g(z)| for |z| = 1.

A:

Q: 10. Consider the function f(x) = x³ + 6x² - 36x + 4. Then I. f decreases on (-6,2) and increases on…

A: Given: To Find: To find the true statements.

Q: 15. The number of points where f(x) = |x|² - 3|x|+2 | is not differentiable is/are (C) 4 (D) 1 (A) 5…

A:

Q: 3.33. Decide which of the following functions are: (a) one-to-one; (b) onto; (c) both; (d) neither.…

A: (1) Given: f: ℤ2→ℤ where f(n, m)=n-m Part (a): One-one function: A function f is said to be one-one,…

Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

A:

Q: 12. Let f(z) =,h z 0. Then f(2 + h) – S(2) h A) – 4+ 2h 1 B)- 4+ 2h C)-- 4- 2h 4-2h

A:

Q: Let H(x):=k for x=, (keN) and H(x):=0 elsewhere on [0,1] Show that H(x) 4ER[0,1].

A: In this question, we use the definition of Riemann integral to check the function H(x) is Riemann…

Q: 4. If f(x, y)=In(2x + 3 e), then- af axy for this function is

A: Find the partial derivative for the function f(x,y)=ln2x+3ey

Q: 2. Let f(x) = -x– 1. a) Find f-1(x).

A:

Q: 8) Consider the end behavior description below. • as x oo, f(x)→-00 • as x → 00, f(x) → ∞ Which…

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Q: Show that o () –1 is an implicit solution to 2 -2y on the interval (-00, 00). Inload our

A:

Q: only need b, d, f, h, j (non-starred problems). Thank you!

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 12. Let f(x) = x + 2 and g(x) = x² - 1. Find (gᵒf)(4)

A: Given two functions 1.f(x)=x+2 g(x)=x^2-1 lets find g(f(x)) at 4

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.