A sufficient condition to use Newton's progressive formula for inclusion is: Xnxo (A) m = |m| < 1 n xo хо - Xn (B)m= m < 1 n Xn -X₁ (c)m -,|m| = 1 , |m|< 1 (D)m = n x1-xn n

Q: a. Let f(x) = (-4x² + 3) (-4x² − 3). - Then f'(x) = b. Let g(x) = 2√√x + 3 x4 +2x² Then g'(x) Hint:…

A:

Q: 36x12. -1. Provide appropriate 6x6 –1 (b) Find the least integer n such that f(x) is O(x") for ƒ(x)…

A:

Q: f (x) = 2x, g (x) = x + 4 and h (x) = 5 – x³ Evaluate the following: 6) (f + g) (2) 8) (f · h) (–1)…

A: Using rules of function.

Q: Derive the 4-point forward formula for f"(x) by using values f(x), f(x+h), f(x+2h), and f(x+3h).…

A:

Q: Use Newton’s root finding method to determine the zeros for the following functions, from the…

A: Introduction: Newton's root-finding method is an iterative method that uses the tangent line to the…

Q: Finally, use the Generalized Power Rule to determine[x -x], noting that x-x is the difference of two…

A: Here we have to find differentiation of f(x)

Q: What are all the roots of f(x) = x* – 3x³ +x – 32 A -1, 3 only 1 ti3 only 2 1tiV3 -1, 3, 2 1, -3, VI…

A:

Q: Algebraically, find the absolute min and max of f(x) =x/1-x on [-1,1].

A: We have to find absolute maxima and absolute minima of f(x)=x1-x at  [-1,1] For doing this first, we…

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: +¹²+z111² Prove that x12 where prime denotes differentiation w.rts. = 1 p² o² + 1+p¹² P

A:

Q: X4 none of these X (c) f'(x) does not exist.

A: f''(x) = 0  at sharp corner f'(x) does not exist for f'(x) = 0 , tangent line is horizontal

Q: Let a be a fixed positive number, not equal to 1. Let f(x) = e-e*. %3D Find the real number x1 such…

A:

Q: iven F(X) = 4X+3, 9(x)= X²-5 evaluate (90F)(1)

A: Given,  f(x)=4x+3, g(x)=x2-5

Q: Solve for r: 3x2 = 4x - 2. 2 + 2/2i (a) 2 + 2/10 (b) 3 3 (c) 3 2士 0 (d) 3 (e) None of these

A: Given,              3x² = 4x - 2

Q: (10,00 Puanlar) Let f(x) = sin 2x. Then find f (999) (x). a) 2099 cos 2x b) – 2099 sin 2x - c) –…

A: Given: f(x) = sin(2x) To find: f999(x)

Q: 1. Expand (r+ 1)(x – 2)(x + 3)

A: We will explain this using commutative law and associative law of multiplication.

Q: sin x -dx 1 7/4

A:

Q: What is the range of the function f(x) = 23 sin 4x+1 ? A B [0, ∞) D [4,16] C) [1,4] [2,00)

A: Range is the set of y values corresponding to x values of domain.

Q: Solve the following difference equation (k + 1)¤(k+1) – kæ(k) (k + 1), x(k) = 0 for all k < 0

A:

Q: Let f(x) = 4x- 1, h(x)= -x+1. %D Find (f o h)(3). (f o h){3} =] %3D

A: Composite function  foh (x) is given by  foh(x) = f(h(x))

Q: x+ cos x 4-lim X-0 \sin x cosx.

A: For the existing limit at the particular point, the Right-hand side limit should be equal to the…

Q: 2. How do you prove a statement of the form ( 3x, P(x) )? Provide examples.

A: To prove a statement of the form (∃x P(x) ), we need to find an example value x such that P(x) is…

Q: 3 را (x) = 2x+7 cl if -5 ²x C1 X = 1 8 If 12X=3 7 11x-2 31 if x > 3 A) use 3-step formula B) is f…

A:

Q: What is the smallest integer a where f(x)=2x is always greater than g(x)=x2 for all x>a?

A: Given  : f(x) = 2x is always greater than g(x)=x2 for all x &gt; a  Implise that :  2x &gt; x2

Q: Q) prove that (1) -2P xSinx 2.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 2) Given: f(x) = (x-1) (x+ 1) was transformed to (x) = (x- 1)(x+ 1)-1. How many roots would the…

A: f(x)=(x-1)2(x+1)2 was transformed to f(x)=(x-1)2(x+1)2-1.