6. Use definition of continuity to determine the value(s) of k such that the 2х + 5, х< 3 function f (x) = kx – 1, x2 3 is continious at x = 3 [A: 4]

Q: Examine the continuity of f(z) = 2-√z+4 Z at z = 0

A: Given: fz=2-z+4z We have to find the continuity of f(z) at z=0.

Q: Prove that (r) = tan(r) is uever negative in 0 <r< and show that g(x) = xsinr decreases…

A: We have to prove that f(x)=tanx is never negative in the interval 0,π2. We hence have to show that…

Q: 17. Show that f(x) = x² +2x is uniformly continuous on the interval [0, 10], using the e -8…

A:

Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: Define h(2) in a way that extends h(t) = (t2 + 3t - 10)/(t - 2) to be continuous at t = 2.

A: Consider the given the function,

Q: The f(x) 6x2 -5x-4 2x2 +x is discontinuous %3D at x = -1/2. By redefine = w , then f will be…

A:

Q: 1. Given that x +1 2x2-1 g(x) Show that the g(x) function is continuous at a = 4.

A:

Q: 1- Discuss the continuity of the following functions at given poin { V9r4+x² 5x2+3x+1 (a) f(x) = if…

A: It is given that

Q: If A(x) = f(t)dt is increasing on [0,10], then f(x) must be increasing on [O,10]. True False

A: Given

Q: Let f(x)=x² -x² +x + 1 and g(x)= 3-х max{f(t):0sx; for 0 s x s 1} for 1 < x s 2 Discuss the…

A: Topic:- Functions

Q: 7. Suppose that f: R → R is continuous at c and that f(c) 0 such that f(x) < 0 in the…

A: Recall the definition of continuity around c .And then choose an ∈&gt;0 to get a δ&gt;0…

Q: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x&gt;1 we have to verify whether or not the…

Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

A:

Q: Q1/ Discuss the continuity of : 1 x+ for x 2

A: Since, you have post multiple question. I am answering first one. Please post again for remaining…

Q: 4 Given that f(2) is analytic at z = 0 and that f G) =, n = 1,2, 3..,find f(2). VE

A:

Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

A:

Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

A:

Q: b- For the following functions prove that ax2 ay2 1- f(x,y) = e-2y cos 2x %3D 2- f(x,y) = Inx2 + y2…

A:

Q: 1. Employ the following methods to find the maximum of f(x) = 4x – 1.8x² + 1.2x – 0.3x* (a)…

A: Given f(x)=4x-1.8x2+1.2x3-0.3x4. To find: (a) find the maximum using golden search method.…

Q: X if x e Q If f (x) is defined on [0,1] by the rule f (x) = < (1-x , if x 4 Q Prove that fof (x) = x…

A:

Q: Suppose f'(xo) = 0, f" (xo) = 0, .…, f(n-1)(xo) = 0 and f(") (xo) > 0, for a C function f. Prove…

A:

Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

A:

Q: Q2) Discuss the continuity at x=2. When: x> 2 x = 2 3x + 1 f(x) : x² + 3 %3D 2x + 1 x< 2

A: The given functionf(x)=3x+1x&gt;2x2+3x=22x+1x&lt;2to check continuity at x=2

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: For f (x) = , given e < 1, what value of d proves the continuity of f at x = 1? (You may assume that…

A:

Q: Let fc Cx)= Vx if osxs 4 c.(x-4)+2 if x>4 denotes a real constant. - where C Show that lim fe (x) =…

A: The function fcx=x,              if 0≤x≤4cx-4+2   if x&gt;4. Where c is a real constant. We have to…

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) &gt; 2      if 0&lt;=X &lt; 1.Is…

A:

Q: Suppose f is known to be differentiable and contains a local extremum at c, then which of the…

A:

Q: 1. Test the continuity of the following functions at given points? -1 -1 Sx <0 2x (a) fx)= X = 1…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: Suppose that f (0) = 2 and f' (x) ≤ 3 for x &gt; 0. Apply the MVT to the interval [0, 4] to prove…

A:

Q: Q4: Discuss the Continuity of following Also find at x = 1 range. and x = 0. Sxx+1 3x+5 -2 -2x+1…

A: a Given function is fx=x+1,    −2≤x&lt;−1x,            −1≤x&lt;03x+5,      0≤x≤2 We have to check…

Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: - 35) Prove that if y=flx)is continuoUS and flx1= 0 when x is a rational number, then f Lx)=0 for…

A: The objective is to show f(x) =0 for all x belongs to R.

Q: Let fn f, where if 0<<! Sn(x) ={ S 2-a if 0<x<1 and f(x) if a = 0 Then lim sup fn (x) – ƒ (x)| =

A:

Q: 2. Consider the function f with domain (-2, 0): 3|22 – 1| if – 2<r<1 2.r2 + 2x – 4 f(x) = 3 if r = 1…

A:

Q: 1. Determine whether k(x) is continuous at r = 3, where %3D x + 3, x 2.

A: Given  k(x)=x+3,  x&lt;0x2+1, 0≤x≤22x,   x&gt;2 To check the continuity we can use the graph as…

Q: Find m so that f(x) is continuous at x = 2. x +4 if x 2 -

A:

Q: Q4: Discuss the continuity of : 1 for x2

A: f(x) is continuous at a point if right hand limit and left hand limit and functional value equal at…

Q: (a) Discuss the continuity of piecewise function, x-7x+12 x 3 at x= 3 using the continuity test. (b)…

A:

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

A:

Q: Assume thatf is differentiable in (-oo, x) and af'(r)N 0 for all a E (-00, 00). Prove that f has the…

A:

Q: 5.11. Prove that the function f(z) = Arg(z) is discontinuous at each %3D point on the nonpositive…

A: Solution

Q: Discuss the continuity in R3 of the function f(x, y, z) %3D x2+ y2+z2 -1

A: Given: f(x,y,z)=1x2+y2+z2-1.

Q: 6. Discuss the continuity for the following functions x+y a) f(x,y) = 4x2-y2-4 x+y b) f(x, y) = %3D…

A: The objective is to discuss the continuity of the functions.

Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.