Let V = D(0, 1). Suppose that f e H(V), f(0) = 0 and |f(z)| < 1 for all z E V. Show that f(z)|< |2| for all z E V. Hint: For 0

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: 5. Define f: R→→ R and g: R → R defined by f(x) = max{-x, x} and g(x) = |x|, respectively. Prove…

A:

Q: Let f(x) = V4 – x². Then Select one: a. f(x) is increasing on (-2, 0) and decreasing on (0, 2) b.…

A: We know that if derivative of a function f(x) is positive (negative) in given interval then f(x) is…

Q: Suppose that f: R20 R20 is defined by f(x) = x². What can we say about f? →

A: Sol:- Given :- f:R≥0→R≥0It is clear that doamin of Function fx ≥0 and Range of function fx is also…

Q: if f(x) is continuous on [a, b], then we can always say that: Select one: O True O False a b a…

A:

Q: Suppose that f'(x) > M for all x E [a, b]. Prove that f(b) > f(a) + M(b

A: Since  f'(x)≥M therefore the function is differentiable and hence continuous let f is continuous on…

Q: 4

A:

Q: If # f(x) > 48 for x [2,10], then b [ f(a) da ≥ 384, where a =2 and b = 10. a Select one: O True O…

A: First I have written a property of integral and easily find the True is correct option.

Q: Evaluate fff f(x, y, z) dV for the specified and B: B f(x, y, z): Z | 8 2 ≤ x ≤ 6,0 ≤ y ≤ 6,

A: We have to find the value of the given expression according to the given information

Q: If f is differentiable on R and f(0) = 1,|f0(x)| < 1,∀x ∈ R. Show that |f(x)|≤|x|+ 1,∀x ∈ R.

A: Note that |f0(x)| &lt; 1 should have been |f'(x)| ≤ 1. Otherwise, the given inequality won't be…

Q: 2. For f (x) 1, g (x) = 1 + Vx, find the domain and range of f / g, and g/f

A: Given: fx=1, gx=1+x

Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

A:

Q: the guotient f(xth) f(a) where h is cortont.

A:

Q: If f(r) is positive then for all 1 <I<2, we have So f(z) dz 7. Select one: O True O False

A: If f(x) is positive then for all 1≤x≤2, we have ∫07f(x) dx≥7

Q: Find the value of the constant c that makes the following function continuous on (-0, 00). са + 4…

A: We will solve the problem

Q: c. Let f be differentiable on R. Suppose that f'(x) # 0 for every r. Prove that f has at most one…

A: We can explain this statement by 2 explainations given below

Q: Suppose that f e H(C) and |f(2)I < eRez for all z. Show that f(z) ce for some constant c.

A: Consider fz=cez for z=x+i y Take absolute value on both sides: fz=cez=cex+iy=cexeiy=cex…

Q: Suppose f(z) is analytic for |z| &lt;= 1, and |f(z)| &gt;=1. If f(0) =1, prove that f(z) is…

A: To prove that the given conditions on the analytic function force it to be the constant function…

Q: If that f is continuous on a sxsb. Let F(x) be any of f(x). Then, f(x)dx = F(b) - F(a). This theorem…

A: Recall: Mean value theorem: If f(x) is continuous over an interval [a,b], then there is atleast one…

Q: Assume that f is continuous on the set of real numbers. Find a and b given that b 3 [ f(x) dx - f₁…

A:

Q: If the function f:R Ris given by f(x) = x for all z E R and the function g:R- {0} → Ris given by…

A:

Q: Let f(æ) = /90 - x and g(x) = x² – a. Then the domain of f o gis equal to [a, b] for a = Preview and…

A: Given: fx=90-x, gx=x2-x

Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.