of a and b 2) A function f is defined as f(x) = for x 1 = - for x = 1. Show that f(x) is differentiable at x = 1 and find its value 3) Let f(x) = if x 2 = k‚ if x = 2. If f(x) is continuous for all x‚ then find the value of k. 4) Let f(x) be a function of x defined as f(x) = ‚ x 1 = ‚ x = 1. Discuss the continuity of function at x = 1 5) Determine
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n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
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Structured program list. First unit: Sets. In this unit the fundamental concepts of the theory of sets is addressed to provide the tools and the language of operation for subsequent units. Second unit: numbering systems. In this unit‚ we address numbering systems of different cultures until the one’s used current day‚ highlighting the importance of ten based numbering system (decimal)‚ which will be developed in depth by tackling its properties through the next unit. Unit Three: The field
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looking for at Store A. In Store A‚ the bracelet without charms costs $85 and each charm costs $15. A. Use function notation that models the total price of the bracelet and how that price is based on the number of charms. Explain the reasoning behind your equation. 15W=85 IN ORDER TO FIND THE NUMBER OF CHARMS YOU NEED YOU HAVE TO DIVIDE. B. What would be a reasonable domain for this function based on this scenario? Explain why this is a proper domain. C. If Marco and his sisters have saved $250
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to evaluate logs‚ trigonometric functions‚ and exponents? This ability is due in large part to the Taylor series‚ which has allowed mathematicians (and calculators) to approximate functions‚such as those given above‚ with polynomials. These polynomials‚ called Taylor Polynomials‚ are easy for a calculator manipulate because the calculator uses only the four basic arithmetic operators. So how do mathematicians take a function and turn it into a polynomial function? Lets find out. First‚ lets assume
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__ The total amount of revenue made by the Miramar Resort Hotel is given by the function ‚ ‚ where x is the amount of money the hotel spends on advertising its services‚ and where both revenue and x are measured in thousands. 1. Using Wolfram Alpha‚ graph the revenue function over the given domain and paste the graph here. 2. Compute the marginal revenue function and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing
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coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic]‚ f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify
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Name: Date: Graded Assignment Checkup: Graphing Polynomial Functions Answer the following questions using what you’ve learned from this unit. Write your responses in the space provided‚ and turn the assignment in to your instructor. For problems 1 – 5‚ state the x- and y-intercepts for each function. 1. x-intercept: (0‚ 0)‚ (-4‚ 0)‚ (0‚ 0) y-intercept: (0‚ 0) 2. x-intercept: (1‚ 0) (0‚ 0) (-4‚ 0) y-intercept: (0‚ 4) 3. x-intercept: (-1‚ 0) (0‚ 0) (0‚ 0) y-intercept: (0‚ 0) 4
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1. 7.5/8 The height in metres of a ball dropped from the top of the CN Tower is given by h(t)= -4.9t2+450‚ where t is time elapsed in seconds. (a) Draw the graph of h with respect to time (b) Find the average velocity for the first 2 seconds after the ball was dropped h(0)=(0‚450)‚ h(2)=(2‚430.4) = (430.4-450)/(2-0) = -9.8m/s √ (c) Find the average velocity for the following time intervals (1) 1 ≤ t ≤ 4 h(1)=(1‚445.1) h(4)=(4‚371.6) = (371.6-445.1)/(4-1) = -24.5m/s √ (2) 1 ≤ t ≤ 2 h(1)=(1‚445
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3. REQUIRMENT ANALYSIS 4. SYSTEM DESIGN 5. SOURCE CODE 6. TESTING 7. FUTURE SCOPE OF PROJECT PROPOSED SYSTEM 1. DISCRIPTION:- a. function used:- i. function are used for formatting line. ii. for reading records. iii. for processing. iv. for calculate percentage. v. to show the result. b. student discription It includes student code‚ name‚ address and
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