Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

Q: Write the equation of the line tangent to the graph of the function at the indicated point. As a che...

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Q: Consider the curve defined by the equation 2x +y 3xy for questions (4-6). 3. 2 -3 -2 -1 1 2 3 -1 -2 ...

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Q: - 10 тх — 12 x2 + 3x – 2 if x > if x < Let f(x) = -10 If f(x) is a function which is continuous ever...

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Q: The function gives the cost to manufacture x items. C(x) = 30,000 + 10x + 50,000 -; x = 100 Find the...

A: Given problem:-

Q: Evaluate the limits. If any of them tend towards-oo or +0o, enter "oo" (two lower case "o" letters) ...

A: Solution: limx→2-3(x-2)2    

Q: Evaluate the indefinite integral 5e" dæ S 5e² dx +C

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Q: V3 2dy 3 у\у2-25 y.

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Q: 4 dx the integrand is x2 In x2 A) True B) False

A: We can find the answer as below.

Q: Let f(x) = (- 3r- 9)* (6z² – 6)5 4 f'(x)=

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Q: Convert the following number in the indicated base. 6701 to base 15

A: Divide the number repeatedly by 15 until the quotient becomes 0. When 6701 is divided by 15, the qu...

Q: (3 +x if x < -1 if -1 sx< 1. (2 - x if x 2 1 Let f(x) = {x2 Sketch the graph of f. y y 3 -3 -2 -1 1 ...

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Q: Consider the function f(x) given by the graph below. y -5- f(x) -5 Determine the limits. If a limit ...

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Q: Find (fo g)(x) and (go f)(x). 1(x) = 6x + 1; g(x) = x (fo g)(x) = (Simplify your answer.)

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Q: Which of the following is/are signified by lim f(T) = co? OAs T approaches a, the value of f(x) incr...

A: limit of f(x) as x approaches a is infinity signifies the following- 

Q: Let f(x)= -6x^4+8x^3+72x^2 a) f has a relative minimum at x= b) f has an inflection point at x= c...

A: Given; Let f(x)= -6x4 +8x4 +72x2   a) f has a relative minimum at x=  

Q: What is the absolute maximum on the curve x2 4х — 7 on the interval [-7, -3]?

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Q: Divide the numerator and the denominator by the highest power of x in the denominator and proceed fr...

A: Firstly , we can divide denominator and numerator by the highest power of 'x' and then find limit.

Q: Consider the region R between y = sin x and the x-axis for 0 ≤x ≤π. (a) Find the volume of the solid...

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Q: The following situation is used in the next five problems Some values for the function f(x, y) are g...

A: Find the limit of the function f(x,y) when (x,y) tends to (0,0).

Q: Find values of c, if any, at which 2x f(x): 15 x + 7 is not continuous (enter as comma separated lis...

A: The rational polynomial function y=fxgx is continuous everywhere except such 'x' where g(x)=0. Given...

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: – 4 a (a) In 6-4c-1 (b) In Vb°c'a 'c...

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Q: cos (a + 8) y= dy Find da dy Immum dx Type sin(x) for sin(x), cos(x) for cos(r), and so on. Use x^2 ...

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Q: Suppose that your best friend has calculated the partial derivatives of a given functionf(x,y)and to...

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 9] for y = x. (Use sym...

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Q: Find the values of c that make f continuous everywhere: ´x² – c² if a 9 smaller c = larger c = Use ...

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Q: (c) log, 2k (d) 74log, 5 – 5 log, 4

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Q: A pebble is dropped into a still pool and sends out a circular ripple whose radius increases at a co...

A: Given query is to find the rate of change area.

Q: Let f(a) = V5z + 2x + 5 f'(x) = [ f'(1)

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: Calculate the arc length of y = 15 – 14x over the interval [1,3]. (Use symbolic notation and fractio...

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Q: Find the indicated derivative and simplify. dy 41 Int for y = - dt et

A: Product Rule of differentiation : du.v.wdt =dudt.v.w+u.dvdt.w+u.v.dwdt.

Q: Let f(x) = 8x + 10 – 3e². Then the equation of the tangent line to the graph of f(x) at the point (0...

A: The given function is: f(x)=8x+10-3ex

Q: T sin(x) cos(x) dæ = Hint:

A: Topic:- integration

Q: 3 The expression VV 729x equals nx" where n, the leading coefficient, is: 3 and r, the exponent of x...

A: To find the coefficient and exponent.

Q: Complete the expanded notation for 62,708,934

A: Follow the procedure given below.

Q: what is the avorago valus OF a Funckon F on an Posterval [a,b]? 13 the given by vallis of Fa)-tan X,...

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Q: Determine amplitude, period, phase shift and the midline of the following function: y = -3 cos (x-)+...

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Q: Use the figure to find the exact value of the trigonometric function. Find cos 20. 3.

A: We can find the value of cos2 theta as below from the figure

Q: 11) sin-! 2

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Q: The figure below shows the graph of a function over the closed interval -25xs2. Complete parts (a) t...

A: Topic:- calculus

Q: 15) tan- -1 Vz 17) cos -1 19) tan 1

A: topic - Inverse trigonometric ratios

Q: 13) sin- 15) tan--1 1/-

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Q: If f(x) = sin(a), find f'(x) Find f'(4)

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Q: sec® tan Od® coso A) tane В sece sec?0

A: topic - indefinite integral

Q: sin2t costdt (A sin2t cost C sin?t D sint E cos?t F None

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Q: How long (in years) will it take a $900 investment to be worth $1000 if it is continuously compounde...

A: Amount = $1000 Principal=$900 Interest rate = 8% 

Q: The number of females in law continues to show steady increases. The number of female lawyers in a c...

A: a. It is exponential function. b. F(30) =&gt;F(30)= .834* x^1.297               =.834*30^1.297      ...

Q: Determine the point on the curve at which the slope is 18. r³ - 9x – y = 0

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Q: 2. Answer C/DC a. lim f(x) x2 b. lim f(x) X-2+ c. lim f(x) -3 -2 -1 -1 X-2 d. lim f(x) -2 X-5 -3 e. ...

A: limx→a f(x)=L if and only if limx→a+ f(x)= L=limx→a- f(x).

Q: + 1)!. approaching the vertices of an equilateral triangle, each circle denominators? Use the patter...

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Q: Evaluate the following indefinite integral | 8 sin(x) – 2 cos(x) dx =

A: We have to find integral