Q3) For what values of a and b are ax + 2b , y = x? + 3a -b, 3x-5, x<0 0 2 Continuous at every x ?

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

A:

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

A:

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - if x 3 a = b =

A: Given that,

Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

A:

Q: Find the values of a and b that make f continuous everywhere. x²-4 if x 3

A: If a function is continuous everywhere Then right hand limit and left hand limit on any point will…

Q: Show that f1x2 Vin x is right-continuous at x = 1.

A:

Q: 4. Use limits to determine the values of a and b that guarantee the function below is continuous.…

A:

Q: Find the values of a and b that make f continuous everywhere. 2-4 x 2 if x < 2 f(x) if 2 s x< 3 if x…

A: To determine the values of a and b so that f(x) is continuous everywhere.

Q: Find the interval(s) wheref (x) =vx+ 2x+6 jis continuous. A) [2, 6] B (-*, *) C) -6, 6] D) [0, -)

A:

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

A:

Q: Show that f (x) = is not uni form continuous on (0,3) -3

A: To prove that 1x-3 is not uniformly continuous on 0,3

Q: Suppose that ?(?) is continuous and differentiable on the interval [0,6], that ?(6) = −7 and that…

A:

Q: Find the largest open intervals where the function is concave upward. 16) f(x) = x3 - 3x2 – 4x + 5…

A:

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

A:

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

A:

Q: Does the MVT apply to f(x) = - on the interval [1, 4]?

A:

Q: f continuous everywhere. f(x) =   x2-4/x-2      if x < 2

A: Given fx=x2-4x-1if x&lt;2ax2-bx+3if 2≤x&lt;32x-a+bif x≥3 fx is continuous everywhere. Aim: Find…

Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: Find all values of c such that f is continuous on (-, 0). 7- a?, { x c C = (smaller value) с 3…

A:

Q: find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable?

A:

Q: If f (s Continuous then on -fex) True or felse?

A:

Q: Find the values of a and b that make f continuous everywhere. x² – 4 if x < 2 x – 2 ax2 – bx + 3…

A:

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

A:

Q: (b). Find the bound for absolute error at x = 2.9 on the interval [x, x,], where x, = 2.25, x, =…

A: On the interval x0,xn where x0=2.25, x1=2.5, x2=2.75, x3=3 with n=3 along with the function…

Q: Determine the largest interval over which the fu Vx+2 is continuous.

A:

Q: Suppose that f(1) = 2, f(4) = 8, f '(1) = 4, f '(4) = 3, and f " is continuous. Find the value of xf…

A:

Q: Every continuous function on a, b, that has absolute extrema on endpoints, must have one critical…

A:

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

A:

Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - 4 if x < 2 X - 2 f(x) = ax2 -…

A: Here, we need to find the values of a and b. We are given that f is continuous everywhere.  So,…

Q: f. Is the domain of f(x,y) = In (3x2 + 3y²) bounded or unbounded? Bounded Unbounded

A:

Q: Q2 Evaluate whether the function 1-xy if xy # 1 z = x-y if xy = 1 continuous at (1,1) or not.

A:

Q: let Peas be delimed by Xく2 3-X I5 fixo continuous V= 2 2.

A: A function is continuous at a point if it's left hand limit is equal to right hand limit and both…

Q: What is the lower limit and upper limit bounded by the curves y 9 - r2 and the line y = x + 7 ? -2…

A:

Q: 8. Use the c, 8 definition to show that fAx) = x? +1 is continuous at

A:

Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

A:

Q: Determine where f(x): V4 - x2 is continuous. Express the answer in interval notation.

A:

Q: Determine local extremum f(x,g) = xy(4-x-). %3D

A:

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x&lt;2ax2-bx+3if 2≤x&lt;32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: Q4) Show that f(x)=|x x<2 3x -2 x2 2 is continuous at x=2 %3D

A:

Q: Determine if continuous f (x) = V4-x at x=0 %3D

A:

Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

A: