4. If the function f(x) is defined by f(x) =-6 then which of the following is the value of f(10)? (1) –1 (3) 14 (2) 2 (4) 7

Q: 1. To show that +2-4= 0is an implicit solution to do Lon the 2y interval (-oo, 4), i. First convert…

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Q: 4) Find the value of the function f (x) given in the table below at the point x = 3 by Aitken…

A: to find the value of fx given in the table at the point x=3 by Aitken method  solution we will solve…

Q: (i) Discuss the continuity of the function f(x)= x^2-3x        if x<2…

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Q: 1 If f(x) = and g(x) =-, 2x +1 1 find f (g(x)) and its domain. - 2

A: Composite function :  A composite function is created when one function is substituted into another…

Q: 2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0…

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Q: 3. Consider the function f(x) = 23 if x = Q if x # Q. Prove that f'(0) = 0. Hint: Apply the…

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Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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Q: 2. Consider the following function: y = f(x) = x" – 14x® (a) Determine in which regions this…

A: A function is increasing or decreasing that is determine by    f'(x)&gt;0 or f'(x)&lt;0 A function…

Q: (a): Find the value of k that makes function continuous at x = 4 f (x) = 7x S2x + 7 x > 4 k x < 4…

A: We will use the definition of continuity at a point to find the value of k

Q: given the function f(x)=4x^3 -5, we calculate f^-1 (x) to be

A: To find the inverse of

Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as a differ- entiable function of the…

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Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as entiable function of the independent…

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Q: 2. Consider the following function: y = f(x) = x" – 14° (a) Determine in which regions this function…

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Q: 1. 2. Which statement about the function f(x): x-3 is What is the domain of the function x+2 f(x) =…

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Q: 4. If f(z) is the principal branch of z3, find f'(–1– i).

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Q: onsider the function: h(x) = 5 for x ≤ -4  2x+ 6 for -4<x<2 5- x2 for x ≥ 2 (D) h(−1) (E) h(0)…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: 3. Consider the following functions: f(z)) = x² + 16 9(=)) = (x – 16)² h((x)) = (x + 1)² – 16…

A: Given: f(x)=x2+16g(x)=(x-16)2 and h(x)=(x+1)2-16

Q: 10. What value of k makes the function {2x - (4(x + k) if x > 2 if x <2 f(x) continuous at x = 2? А.…

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Q: 2. Find the x-coordinate of the point(s) of discontinuity of the following functions -16 x3 16х — 4,…

A: For x&lt; 3 , f(x)= -16 is continuousFor 3&lt;x&lt;6 , f(x)=16x-4 is continuous tooFor x&gt;6 ,…

Q: The function h(x) 1 can be expressed in the form f(g(æ)), wher x + 4 defined as: f(x) =

A: The function h(x)=1x+4 can be expressed in the form f(g(x)), where g(x)=x+4 We have to find f(x) = ?…

Q: 8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

A: h(x) is given. We have to find h(2), h(0) and h(-x)

Q: 2.Find an example different from the one in the text showing that (f ∗ 1)(t) need not be equal to…

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Q: Determine all critical points for the following function: f(x)=12x^2+2x^3

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Q: Given f (x) = sin (z) and g (x) = x, the graph of the combined function h (x) = f (x) g (x) most…

A: Given  f(x) = sin(x) and g(x) = x

Q: 1. Fit the function g(x) = v1x + v2 (x – 1)3 to the data in table below. Xi -1 1 Yi 2 1 -1

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Q: For what value of the constant c is the function f continuous on (-o S cx2 + 8x x3 – cx if x 3 с 3

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Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

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Q: Suppose thatƒ (1) = 2, that f ' (x) is the function shown in the graph below, and that k (x) = f…

A: Equation of tangent line : y - y0  = m ( x - x0 )  m is the slope of function . And ( x0 , y0 ) is…

Q: 1. If 2. If f(x) = 5x- 3x² – 2x + 7 f(x) = x* In x find f'(x) and f'(1). find f'(x) and S'(1).

A: Given:  1. fx=5x4-3x2-2x+72. fx=x4ln x

Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

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Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

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Q: 3. Consider the function f(x) = -{2 if x = Q -r³ if x # Q. Prove that f'(0) = 0. Hint: Apply the…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: -4 2 3 For the above function f( x ) = 2 · 1.5, estimate f'(x) using h = 0.001 for the following…

A: Given that f(x)=2×1.5x and h=0.001

Q: Do you agree with the contention that the functions f(x) = x + 2 and g(x) = x2 − 4/x − 2 are the…

A: I am not agreed with this fact that f(x) and  g(x) are the same in every respect. The reason behind…

Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

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Q: The function h is defined by h(x) = x^2 +2. find h(5z)

A: Given h(x)=x2+2

Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: 1 Use the functions given by fx) 1 and g(x) = x' to find (fº g)¯- %3D X - 125

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Q: 2. If f: R→→ R satisfies f(1) = 3 and f'(x) ≥2 for all x's, how small can f(7) be?

A: Here we have to find the smallest value of f(7).

Q: Evaluate: g(f(-3)) y fx) y = g(x) 10 10 6. 3 3456789 10 10-9-87-6 "5 -2 -1 2345678 9 10 -2 -4 to

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Q: Find the rule of the function associated with the following table. 1 3 y 1 4 9 Oy = x² y=x 1 | Oy…

A: As observed feom the graph, we have squared each of the quantity.

Q: 3. Do you agree with the contention that the functions f(x) = x+2 and g(x) x-2 are the same in every…

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Q: (2ł – 5) 7 (n² –5) For the function f(x) , find ƒ=1(x). - f- (x) = V (x + 5)° Of-'(x) = Væ5 + 5 O…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x − 2 on the interval [3, 7], how many…

A: We have to apply Rolle's theorem.

Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 20x – 9 on the interval [3, 7], how many…

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Q: 1. If h(x) = (f(x))² - (g(x))2,f' (x) = -(x) and g' (x) = f(x), then h'(x) = %3D

A: Given h(x) = (f(x))2-(g(x))2 On differentiating both sides , we get h'(x) = 2f(x) f'(x) - 2g(x)…

Q: If we apply Rolle's Theorem to the function f(x) = 2x – 12x -7 on the interval [1, 5], how many…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: