b) Suppose f(t) is piecewise continuous on [0, 0) and is of exponential order. Of the two images below, which one is the only plausible one? Explain. s2 + 42 s+T L{f(t)} = L{f(t)} = 3s2 3s2

Q: The range of f(x)=/4-x² is [0,2] O (-00,2] [2,0) O [-2,0] [-2,2]

A: Range :- set of all output values

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: 2. If f(x) = xe, determine f(2018) (r). (A) (x - 2017) e (D) (x+2018)e* OA OBO OD OE (B) (x+2017) e…

A:

Q: 6. Use algebra to determine whether the given functions are is even, odd or neither a) f(x) = -x³ +…

A: For a given function f(x)  If it satisfies the condition  f(-x) = f(x), then the function is Even.…

Q: 02: Let f(x)= x' – 7x+ 2, 0sxs1. 1. Show that f(x) has exactly one real root in the indicated…

A: Answer

Q: (a) Given Ax-6, x6. (i) Calculate the value of A. (4 marks) (ii) Examine whether the function is…

A: Continuity

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

Q: (2ax + 4,x < 2 g(x) = 110, 7. Find the value of “a" if gx) is continuous for all 2 < x real numbers.

A: g(x)is  continues for all real numbers

Q: Find number k so that f(z) = 10x + 8 x -1 is continuous on (-0,0). O -2 4 -4

A:

Q: What are the valuesbof x where tge functions f(x) = (3x+2)(x+1)\x+3 is undefined?

A: Consider the function f(x)=(3x+2)(x+1)x+3

Q: Find the values of a and b that make f continuous everywhere. b = f(x): x-2 ax² - 6x + 3 4x -a + b…

A:

Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

Q: (x2+3). Explain why √x4+24 Q7. Consider the function f : [0, 1] → R, x→ (a) f continuous, (b) f is…

A:

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

A:

Q: A/ Derive by definition: y = Vx - 3 ? B/ Determine the value of (z) and (k) that makes the function…

A:

Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

Q: Evaluate Hint: Use differentiation to show that n=1 (1 – x)-2 = nx"-! (for |x| < 1)

A: We have to show that 1-x-2=∑n=1∞nxn-1

Q: Compute f(5) (e) forthe function f(x) = x³.In(x+)

A: f(x)=x3.ln(x4)f(x)=4x3ln(x)Differentiatef'(x)=4x2+3x2ln(x)f'(x)=4x2+12x2ln(x)Differentiatef''(x)=8x+…

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

A:

Q: Find a and b so that f(x) is continuous if f (x) = Ⓒa = ²/1 b = 60 96 a = - ²/2 b = 29/4/20 -²/26 =…

A: