12. If a function f is continuous in [a, b] and c e ]a, b[ such that f (c) # 0, then there exists some 8> 0' such that f (x) has the same sign as flc) for all rs lc -8 c+ 8r

Q: (1 2 ) x, (а). | 0 5 6 (7 0 2 3 X2 1 X3 2

A:

Q: O O O OC Find (all) the value(s) of c such that 5c2n 20 3 n=0 (A) c= 2 (B) c = 7 (C) c= -2,2 (D) c =…

A: An infinite series has the form ∑n=0∞ anxn=a0+a1x+a2x2+a3x3+…… where ai's are constants. We have to…

Q: div(f F)= f div F + F f

A: If we can show that left side of the equation is equal to the right side of the equation, then we…

Q: Proof fourier transforms? ax e Caz0)

A:

Q: 0 -15 Figure 4 The real number system 13 Copy and complete the table. The first row has been done…

A: N0 is the natural number including 0. Z=...,-2,-1,0,1,2,3,... Q is the set of rational number. Q' is…

Q: Proof Prove Property 1 of Theorem 1.2.

A: Given :                  The limit,                 limx→c f(x) = L Formula used :…

Q: IWe Eam write the Preriunf proferties by Corter's चि f0li~4+ = ९ ए-ो Pronk

A:

Q: UANTIFICATION  True or False  FOR ALL y, y is any integer: y^3 - 1

A: Given expression is  y3−1=0 To determine whether y is an integer or not for any value of y.

Q: Age Social media user Non-social media user Total Younger (18−22)(18−22)left parenthesis, 18, minus,…

A: The given data is as follows, Age Social media user Non-social media user Total Younger(18-22)…

Q: Direct and Indirect Proof 1- ~a->f 2--g->b 3--f->e 4- (bva)->-f 5-c->d 6-e->~(~g->d) 7-8->c ...…

A: A direct proof, also known as a positive proof, is a method of proving a statement by establishing a…

Q: Complete the following formal proofs. 1. (C > D) ^ (E →F) 2. (F^D)→ G 3. -G 4. -(F^ D) 5. -F v -D 6.…

A: We fill the blanks of the given formal proof by using rules of inference.

Q: 1. Consider the basis B = {(2, –v2), (2, V2)} for R². Define (ỷ, 2) =y,2 +y22. %3D a) Verify that B…

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Proof the empirical rule in detail and with an example

A: The objective is to prove the empirical rule and give an example.

Q: Prove that A CB P(A) C P(B).

A: We have to prove that

Q: → P2 be defined by 18. Let L : L(p) and Dim (Domain(L))? : P4 p". What are Ker(L), Range(L).

A:

Q: 0.3(0.2x *+6) =0.2(0.25

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Using Reciprocal Substitution * For S x²(®1+x+j{ 1 4(81t* + 1)3 81(81t* + 1)5 O Option 1 Option 2 1…

A: The given question is related with integral. We have to find the integral ∫dxx281 + x434  by using…

Q: 2 Prove that it a) = (a+b) = (- 1/(-a)= -( - عاها - (a+b) = (- (-a7²b) + (a+b))

A: To prove these properties, you can use the properties of real numbers and basic algebraic…

Q: 2n + 5n Zn=1 3n

A:

Q: If x has a value of -4, determine if the series converges (absolutely or conditionally) or…

A:

Q: QUANTIFICATION  True or False  FOR SOME y, y is any integer: y^3 - y^2 -y = -1.

A:

Q: Find (all) the value(s) of e such that 20 (A) e=2 7 (B) e= (C) e=-2,2 (D) e= (E) =-}} (F)c=;

A: Simplify the series,  as follows.

Q: Part B: Calculus and proof (i) Let f(x) = e* - 1 - x. Using calculus-based approach prove that…

A: Given :let f(x)=ex-1-x using calculus based approach prove that ex>1+x for x>0

Q: Given: X, + X2 + X3 = 5 X, + 2X, + 2X3 = 6 X, + 2X2 + 3X3 = 8

A: This is a problem of Cholesky's decomposition and linear transformation.

Q: If Lar 98n+2 then > 99ar 99n+3 %3D k-2 k-2 O 99 100

A:

Q: Prove that there is no permutation a such that al(12) a = (34) (15).

A:

Q: Consieley (1- Eq +B) - (6,rtd +B(1+Y)gm! +Br y = 2(6,-6)+ S,+&a →O Determine condition under which…

A: Question: Under which condition yk=ηε1-ε2+δ1+δ21+ε2γ-1-ε1γ-α is the equilibrium point of…

Q: • Error and Q Functions 1, Use the definition of error functivn, prove that

A: We want to solve the given problem.

Q: Transformation of ₂F₁ : If x < 1 and X X < 1; then: 2 Fi (a, b; c; x) = (1 − x)¯`ª₂ F₁ X (a₁c-bi ₂…

A:

Q: Prove that  If c ∈ Z, then c^2 +3c+4 is even. Show your solution

A: Given that c∈Z Prove that c2+3c+4 is even

Q: f(2)de = Af(1)+"(), the If Af(1) + 3 0. A = 2, B 1 O A = 0, B = 2 O A = 1, B = 1 O A = 0, B = 1 O A…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: S Y 4 - (0 (2.4) -4 25 O 3 (-4,1) (4,-1) X what is it called t

A: Given query is to find the point which lies in the solution region.

Q: theory Prove it

A:

Q: Reduce a fraction show all work

A: Consider the provided fraction,

Q: △-マ= △Y AV MS A(4全)+) 山natn- fnbun %3D an)

A: Property a: ∆-∇=∆∇ Note that, ∇fx=fx-fx-h∆fx=fx+h-fx