Let f:R →R ond q: R→ R. Define the pointwise sum f+g as follows! frg= {CX.y): XEIR and y=f(x)+g (xl3 Druve that f+g is a functren from A to R.

Q: 1 nt) Consider the function f(x) = 6x2 +3 is concave up for x E isqrt6/6, infinity is concave down…

A: The concave up and down nature of the function is determined by the sign of the second derivative of…

Q: Use the parallelogram method to find the following sum v + w when v = (-5, 4) and w= =(5, 4). (0,0)…

A: We have to find the following sum v + w, when v = (-5,4) and w = (5,4) by using the parallelogram…

Q: 2x-1 Find f1) if Az) = %3D x+2. a) O b) O c) O d) 515

A:

Q: f:1→1, (f(a)), =1 if n = 0 = n-a, – 1 if n= 0 (f(b)), = b, find b2010 - %3D

A: Given: f(a)n=1 if n=0nan-1 if n≠0and f(b)n=bn To find: b2010=?

Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: Aforce F: 2i+j-3K is applied to a space craft with Velocig V. 3L-J- Express FasThe Sum of aretor…

A: F = 2 i + j - 3k,v = 3 i -j

Q: 0 eg put (1) in f|L) = < ² cos(21), 3 siu (22), A 3√5 355 255 f(2)= < 3105 |24] 3sin (22) L

A:

Q: Verify that fxy = fyx for the following funtion.  f(x,y) = ex + y + 1 fxy = ? fyx = ?

A: Given,            fx,y=ex+y+1

Q: Let f : Nx N → N be a function defined by (n + 1)m(m + 1) f(n, m) = Answer the following questions.…

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Q: Frid the Feurier tranghrm XC10) for the Pulse y the Sapual deitribed bekw: 2, -3mms <t<o X(+) 12,…

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Q: Let f(x) = (x + 2)(x + 1)x (x – 1)³(x- 2). To which zero of f does the bisection method converge for…

A: since you have asked multiple questions so as per guidelines we will solve the first question .To…

Q: #12- Fnd the indefinite integral of the follaung funchon and check the result by differentionion.

A:

Q: KB is ∀xy F(x, y). Prove using resolution-refutation that ∀xy F(y, x).

A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

Q: n = 2 r xF + Σ Σ rx F Trx i=1 i=1_j=1 (r × F) + (r, × F)

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Q: Show that has a continuous extension to x = 2, and find that extension.

A:

Q: 1. Consider the matrices A₁ 4 = ( 1 ) - 1 3 0 A₂ 42 = (3-2) ₁ 4₁ = ( 2² -2²), , A3 0 -2 These…

A:

Q: Write the formula of partial derivation with respect to x?

A: Partial derivatives  Let  f(x,y) is a function given , in which f(x,y) partially depends on x and y,…

Q: Consider the function g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even. Is g continuous…

A: Given function is g :ℕ→ℝ  where  g(n) = 1 if n is odd and g(n) = 2 if n is even.

Q: 3. Let A be the set of all functions ƒ : 0, 1] → R that are continuous in the interval [0, 1].…

A:

Q: Consider the function f(x) = 12x5 + 45x4 - 80x³ + 3. f(x) has inflection points at (reading from…

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Q: 1. If f is an increasing function on (a, b) and P= (ro) is any partition of [a, b], prove that sup…

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Q: The real part of sech (2-j3) is -3.7245 -3.5906 O 0.0403 O -0.0106 -0.5309 1.0357

A: The Euler's formula is widely used formula in complex analysis. It makes a bridge between the…

Q: ?-t-20 f(t)= 12+7t+10 is piecewize continuous on [0,10]. True O False

A:

Q: Find f') if Aæ) = VE+2. %3D a) 0.5 O b) -0.5

A: We can solve this differential as below

Q: |x+5| 2.5.30. Is the function f: R –→ R , f(x) = bounded x + 5

A: Given that the function fx=x+5x+5 To check the function is bounded. Note that: The modulus of x  is…

Q: Find the value of ſ (2x – x³) dx by evaluating it as the limit of sums.

A:

Q: (c) s²+1 s(S-1)³

A: We do the partial fractions first and then find the inverse laplace transform. The detailed solution…

Q: f(x) = 3x - 2sınx +7 %3D aluse the intermediate Value Theore m to show that flx) has at least one…

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Q: We know that the function in the image attached below is not injective but is surjective. Proof why…

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Q: 2-1n 7LX1, Show that the distinct polynomial s x+x and x+X determine the Sange function From Zz bo…

A: We have to show that,  the distinct polynomials x4+x  and x2+x in ℤ3x determine the same function…

Q: Let f(x) = x³ - 10, x= [-15√3, 15√3]. Find the value of c guaranteed by the Mean Value Theorem on…

A: The given function fx=x3-10, x∈-153, 153. We have to find the value of c guaranteed by the Mean…

Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…

Q: Q5:111M) A) Let f: [0,2]R be defined by (3 if xEQ if xeQ fx) = (2) feRn [0,2]. Show that (1) / is…

A: This question is related to limit and continuity .solve in step 2.

Q: : Find the value of k that makes function continuous at x = 4 %3D 3x + 6 x > 4 f(x) = 6x – k x < 4 -

A: To find: The value of k

Q: uestion 6: Suppose f: N N has the rule f(n) = 3n²-1. Determine whether f is 1-1.

A: