If x = 0.8, then [x] – x = 1. -0.8 2. -1 3. -1.8 4. 1

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =    cx2 + 6x…

A: fx=cx2+6x     if x<3x3-cx       if x≥3 fx is continuous for all x<3 & x>3, because it…

Q: For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) =      cx2…

A: The function f is defined by: The definition of the function changes at x=5So the function is said…

Q: In(7æ) Given f(x) = 7 the derivative f'(x) is. 1 7x 1 7 7 7x 1 7x

A:

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

A: Given fx= x2-4x-2 if x&lt;2ax2-bx+1   if 2≤x&lt;34x-a+b      if x≥3Here f is continuous everywhere…

Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x&gt;5 We have to find the value…

Q: (- 0,a) is measurable.

A: Note that, every interval is measurable.

Q: Find a formula for f(") (x) if f(x) = e-10: fln)(z) =[]

A:

Q: 4 ,5 Let f(x) = 7x* In(x) f'(x)

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Q: The derivative of the function f(x) = In 5x is 1 x In 5 Select one: O True O False

A:

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: For what values of a and b is -2, f(x) = { ax – b, -1 <x< 1 3, continuous at every x?

A: Given: fx=-2,    x≤-1ax-b,    -1&lt;x&lt;13,   x≥1

Q: For what value of the constant c is the function f continuous on (-0, 00)? C =

A:

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

A:

Q: if x = 0 11. f(x) = x - 1 if 0 < x < 1 In x if x = 1 et

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

A:

Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: Suppose f(x) = x+x+1 In(x)e²+2· Find f'(x). E Please select file(s) Select file(s)

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Q: For what value of the constants A and B is the function f continuous on (-∞, ∞)? A√x+6-1 for x 3

A:

Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

A:

Q: . Compute f(x) dx ƒ(x) = { 2x if x < 1 4 if x ≥ 1

A:

Q: For what value of the constant c is the function ƒ continuous on (-∞, ∞)? cx² + 2x if x 2.

A: We know :- Limit definition at x=a  ⇒limx→a-f(x) =limx→a+f(x)  if function continous at x=a then…

Q: For what value of the constant c is the function f continuous on (-, o)? cx2 + 8x if x 3 C =

A:

Q: 45. For what value of the constant c is the function f continuous on (-∞, ∞)? Scx? + 2x if x 2

A: Let f(x)=cx2+2xif x&lt;2x3-cxif x≥2

Q: For what values of a and b is ах + 2b, x² + 3a – b, Зх — 5, 0 2 |continuous at every x?

A: Given:

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 6. 2. If f is continuous and f(x) da = 4, find af(x?) dz.

A:

Q: If f(x) = 7cos(x), what is f'(x) ?

A:

Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: Find a formula for f(n)(x) if f(x) = e' -3x fln)(x):

A:

Q: 31. If f(x) = In(x + In x), find f'(1). %3D

A: It is simple differentiation  problem.

Q: Calculate M6 for f(x) = 5 · In(æ³) over [1, 2].

A: Given:   f(x)=5.ln(x3) over [1,3]

Q: Is defined for some value of s?

A:

Q: If f(z) = 4,/ In(x), find f'(x). Find f'(2).

A: Given function:fx=4xlnxWe need to find f'x and f'2.We will use the following…

Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: For what values of a and b is -2, - b, -1 < x < 1 3, f(x) = ах continuous at every x?

A:

Q: If ɛ ER and the function f(x) = ex – 1+ x² is increasing x E R, show also that e >

A: Since f is increasing hence f'(x) &gt;0 for all x

Q: Determine f-¹(x) if 1 (X) = Or¹(x)=x2 X+2 X-3 X-2 or¹(x) X+3 Or¹(x)= X-1 3x + 2 3x + 2 X-1 OM(x)=)…

A:

Q: Show that div (r x a) = 0

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Q: Let f(x) = ex . Then f(n) (0)    ???????

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Q: Derive the following function 9. y In x+1 x-2 10. Dºsin(x)

A:

Q: – one function from X into

A:

Q: (- 0 ,a) is measurable .

A: Given a statement

Q: Suppose that o f (x) dx = 3. Find L f(x) dx if, %3D

A:

Q: a) Suppose that f(x) = 4x if x<-1 = cx + d if – 1<x< 2 = -5x if x 2 2 Find values of c and d such…

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Q: If 5х + 3,х <2 { h(x) = 2x2 + 5,2 < x < 4 Is h(x) continuous at (x=2)?

A: We use definition of contunity

Q: x²-a if x2 is continuous at x-2, then x+3 if x-2 If the function fo)

A:

Q: 2- Find ( for: y= esin-1 x

A: first derivative of function

Q: If |ƒ(w) - ƒ(x)| &lt;=|w - x| for all values w and x and ƒ is a differentiable function, show that…

A:

Q: Find f(t) if L(f) = 6(1-e^(-πs))/(s^2+9)

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.