g) Describe the behaviour of y=-2 x 4x+¹-6 as x → +∞o.

Q: Given lim f(x) = 16 and lim_g(x) = -12, evaluate lim_[5f(x)-3g(x)]. X→-5 X→-5 O a.) lim…

A: Topic - Limits We are given, limx→-5f(x)=16 and limx→-5g(x)=-12we need to findlimx→-5[5f(x)-3 g(x)]

Q: 0.016t 1 The population of a town is increasing at a rate given by P'(t) = 55 e where P is the…

A: Given population, function is an exponential function And population counts start from 1990 So at…

Q: h(y) = et. In (g) Find b'(a)

A: Topic:- calculus

Q: Logarithms turn multiplication into addition. That is, the logarithm of a product of two…

A: We know:- lnmn=lnm+lnn

Q: 82t An epidemic is growing in a region according to the rate N' (t) = +3 I where N(t) is the number…

A: Topic- Differential equations We are given,   N'(t)=82tt2+3where N(t) is the number of people…

Q: Define what is a family of curves/solutions. How is it different from a particular solution?

A: Topic:- calculus

Q: Use the limit definition of the derivative to find f'(x) when f(x) = -2x².

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Monthly sales of a particular personal computer are expected to decline at the following rate of…

A:

Q: How is the inverse of 4sin(x)+7 = f(x)-74x=sin-1f(x)-74 ?

A: The given function is; f(x)=4sinx+7.

Q: An airplane traveling at 600 mph at a cruising altitude of 6.5 mi begins its descent. If the angle…

A:

Q: 45. π/2 So xsin x dx

A: Given integral I=∫0π2 x2 sinx dx

Q: Evaluate 3x + 21 (x + 5)(x − 1) Ta - dx

A: Given: ∫3x+21(x+5)(x-1)dx

Q: Solve AABC subject to the given conditions, if possible. Round the lengths of the sides and the…

A:

Q: A plane flying horizontally at an altitude of 3 miles and at a speed of 692 mi/hr passes directly…

A: Topic- Application of derivatives We are given, y=3miz=8.9 midxdt=speed of plane=692mi/hrand from…

Q: Evaluate the limit: 1-cos 5h h lim ㅠ h+2

A: Given query is to find the limit of the expression.

Q: 3. Let L₁ denote the tangent line to the graph of the function f(x) = x³ - 2x² - 1 at the point (1,…

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Q: d Find (sin 2x) using sin 2x=2 sin x cos x dx d dx (sin 2x)= Express the derivative of sin 2x in…

A:

Q: The revenue (in millions of dollars) from the sale of x units at a home supply outlet is given by…

A: The revenue in millions of dollars from the sale of x units at a home supply outlet is given by…

Q: Check here for instructional material to complete this problem. Find the y-intercept of y = 4x. The…

A:

Q: Find the volume of the solid generated when the region 1 bounded by y = x(6 - x) } Y = 0,x = 3, and…

A: The given curves are: y=1x6-x, y=0, x=3 and x=5 So, the bounded region is as shown below. Apply the…

Q: Write a function of the form y=A sin (Bx-C)+D that has period 4, phase shift -1, and the range -12…

A: Write a function y

Q: Let function g (x,y) = 3x + y ln y sin (1 − x) Assume z as function differentiable E : zy + y ² = at…

A: According to the Bartleby guidelines, I'm answering the first question for you. Please re-post other…

Q: d) √9x x √16x e) 5logx + 2logy - logx f) (3x + 7)²(3x + 7)6

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Q: Calculate the definite integral by referring to the figure with the indicated areas. ff(x)dx 0 Area…

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Q: A can of soda is placed inside the refrigerator. The soda has an initial temperature of T = 70-F.…

A:

Q: Differentiate the function

A: The question is differentiate the function G(t)=5t+7t This can be solved using the formula…

Q: Which one(s) of the following is(are) the Taylor series for the function f(x) = sin(x) about x = ο ?…

A:

Q: Check here for instructional material to complete this problem. Find the approximate slope of the…

A: Given query is to find the slope of the line and determine whether it's increasing or decreasing.

Q: (a) The unit circle is the circle centered at 0,0 (b) The equation of the unit circle is x² + y² = 1…

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Q: Write the first expression in terms of the second if the terminal point determined by t is in the…

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Q: what is b = to

A: We know d/dx(xn)=nx(n-1) , for any real n   Slope of a tangent line of a curve y=f(x) at a point…

Q: Find a Cartesian equation for the curve defined by the following parametric equations. Sketch the…

A: Given that       x = 2 - cost , y=1+2sint

Q: The derivative of f(x)= (4x√+5)(1/x+4x^6) f′(x)=

A: Topic:- function and it's derivative

Q: Proof 5.5: ★ Prove S Σ()(2)-() k>0 n

A: Since you have asked multiple question, as per company policy will solve the first question for you.…

Q: Find T(e) if r(t) = (t, 5, In t)

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Q: For the function: Show work. 9. a. Find the intervals on which it is increasing and decreasing. b.…

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Q: 7 Calculate (4x + x²) dx, given the following. 40 [(42+x²) 2 √x²dx 2 335 3 8 |-- dx = 7 S(4x + x²)…

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Q: Find the derivative of f(x) = (sin³2x + cos²3x) 6cos(2x)sin²(2x)-6cos(3x)sin²(3x) O-6cos…

A: Formulas we use: fgx'=f'gxg'x fxn'=nfxn-1f'(x) cos(ax)'=-asin(ax) sin(ax)'=acos(ax).

Q: X x50] xt) vis OLY wll

A: Evaluate it :     limx→0sin(7x) cos(x)x

Q: Let f(x)=2-xe^x/2x+e^x. Find f'(0)

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Q: III. Determine the rate of change of the function g(x, y) = y² tan(x - 2y + 4) at the point (7,2) in…

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Q: Which piecewise function corresponds to this graph? -6-5-4-3-2-1 9 8 7 65 4 3 N ادانان -1 -2 -3 -51…

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Q: Given f (x) = x³ – 3x, What is the rate of change between domain [1, 3]?

A: Given f(x)=x3-3x

Q: Consider the following points: A(1, 1, −2), B(−1, 2, 1) and C(1, 0, 1). Determine the parametric…

A: We have to find the line passing through the point B that is perpendicular to the vector AB→ &…

Q: Prove the following trigonometric identities. 1. tanA+secA-1 tanA-secA+1 = 1+ sinA COSA

A: tana+seca-1tana-seca+1=1+sinacosa since you have posted multiple questions i can do first question…

Q: with

A: Please refer to the image below

Q: 29. A 10 ft tall fence runs parallel to the wall of a house at a distance of 4 ft. Find the length…

A: Formula: In right angle triangle Cosx= Adjacent side/hypotenuse Sinx= opposite side/hypotenuse

Q: dt (2) Evaluate showing all steps the indefinite integral 14. (In evaluating the integral you may…

A: The given integral is 1/(1+et).

Q: Consider the following points: A(1, 1, −2), B(−1, 2, 1) and C(1, 0, 1). Determine the parametric

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Q: Find the missing coordinate of P, using the fact that P lies on the unit circle in the given…

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