1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to the curve f(x) = x² + 3x at the point where x=2.

Q: _t f'(x) = tª – t3 + t² + t – 1

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Q: sec2zydy Evaluate the integral: Jtzy(3+tan-zy) A. In(3+ tan²2y) +C In(3+ tan?2y) +C In(3+ tan 2y) +C...

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Q: ow directly that the given functions are linearly dependent on the real line. That is, find a nontri...

A: Topic:- algebra

Q: Determine the positive real root of In(x) 0.7 using three iterations of the Newton-Raphson method, w...

A: Using Newton rapshan method

Q: Write the first five terms of the geometric sequence whose first term is 8, and whose common ratio i...

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Q: Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at (0,...

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Q: Lind ds 6) 5. 52+w²

A: It can be solved using chain rule and divide rule of differentiation.

Q: A particle travels along a horizontal line according to the function s(t) = -3t° +t² + 3t – 2 where ...

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Q: Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = - 1- 2x Provide your a...

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Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral 

Q: 3n 2n TE S. (sin x + cos y)e dx dy dz A. 2n(e2n + e3) B. 2m(e2 – e3") c. 2m(e + e2") p. 2n(e- e")

A: For the solution follow the next steps.

Q: Evaluate A. 1 B. 3 C. 2 D. 4

A: The objective is to evaluate the integral.

Q: Consider t=[−6, 2] and s=[2, 2] a) Without determining the angle between the vectors, determine whe...

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Q: C. How long is the ball in the air? i. Describe how you read that off the graph ii. Describe how you...

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Q: Graph f (x) = (1/2)* and g (x) =(1/2) ~*+3. Plot three points and also the asymptote.

A: The answer is in step 2.

Q: Find the integral of (1 2x) e^ (-x) dx from x-0 to x=. с. 2 А. 3 в. 4 D. 1 O B

A: ∫ uv dx = u ∫ v dx - ∫ (u' ∫ v dx) dx. ∫ (1+2x)e-xdx = -(1+2x)e-x + ∫2e-xdx ∫ (1+2x)e-xdx = -(1+2x)...

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

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Q: ) .3 Find the derivative of h(x) = cos (2x – 5 %3D

A: Given,            hx=cos42x3-5To find : The derivative of the given function.

Q: Let k(x) : (4x-)g(x)h(x). Given the following table of Val %3D -1 1 3 h(x) 1 -3 0. 3 g(x) 3 -4 0. h'...

A: topic - derivatives

Q: then the distance from a point P to the line L is equal to the length the component of the vector AP...

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answ...

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Q: Use Cramer's rule to solve the system. 4x - 2y - z= - 6 3x - 5y - 5z -6 2x - 3y = 2 Write the fracti...

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Q: Find the derivative of f(x) = log(-6x* – 6x + 5) at the point x = 2. Provide your answer below: f'(2...

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Q: 3 Find the equation of the tangent line to f- at the point P (-3, 1) for f(x) = :-1 %3D 1- 2x Provid...

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Q: The function f(x) = 6x¬1 for the interval (1,3) has a local minimum. a local maximum. both local min...

A: Note :- As you write for solution only for interval [1,2] so i  am providing solution only for it.

Q: General Solution of a First Order Linear Differential Equation A first order linear differential equ...

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Q: (a) The maximum carrying capacity of a park is 100 animals. Currently, there are 10 animals in the p...

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Q: Use Disk Method or Washer Method (for all parts) to set up an integral (without the absolute values)...

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Q: General Solution of a First Order Separable Differential Equation In this problem, we want to find t...

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Q: Consider the following tables: -2 -1 1 2 f (x) 5 -3 4 3 -2 -1 1 g (x) 5 1 3 Fill in the blanks with ...

A: Function values of f and g are given, we have to find the following.

Q: x cos r+ sin r -dr. Find x sin r 5.

A: The given integral,     ∫x cosx+sinxx sinxdx

Q: The rate of U.S. per capita sales of bottled water for the period 2007-2014 could be approximated by...

A: Here we will find the total US sales of bottled water from start of 2008 to start of 2010,

Q: Suppose that an is a convergent series, with positive terms (i.e., an >0 for all n). n=1 (a) Does th...

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Q: Solve in digital format please If the side of a cube measures 24 cm, calculate the approximate incr...

A: Given query is to find the increased in volume.

Q: Given a function f(x,y,z) = (x+9) In (3y - 5) sin (4z). Find the domain of the function. o a. { (xy,...

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Q: 3. Let f(x) = 1+x + x² + x³ + xª + x5. (a) ) Pind T3(x), the Taylor polynomial of f at x = 0 with de...

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Q: Find the derivative of y = cos³*+8 (x). Provide your answer below: y =

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

Q: 5 k3 d. + 2225 k k=1 k=1 п е. + 2n \n k=1 3.

A: We have to find summation of given series. 

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Mini...

A: This is a problem of maxima and minima. Based on the general formula we will find out the value.

Q: [3] Write the expression below as an algebraic expression in x for x > 0. cos(2 tan x) = -1

A: This question is based on trigonometric ratios.

Q: Let F(#) f(/(=)) and G(r) =(F(2))2 and suppose that f(5) = 6, f(6) = 3, f'(6) = 7, f'(5) = 15 Find F...

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Q: Suppose the graph of f(x) is given. Describe verbally how the graphs of the following functions can ...

A: a. fx+4vertical shift up 4 units. b. fx-4Horizontal shift right 4 units.c. 4fx vertical stretch d. f...

Q: Assume that the domain of f and f -1 is (-∞, ∞). Solve the equation for x using the given informatio...

A: We need to solve equation for x.

Q: 2. Solve the following differential equations. (a) y' = x2 - xy +1. (Hint: Consider the subsitution ...

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Q: a. For the following functions and values of a, find f'(a). b. Determine an equation of the line tan...

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Q: A. The population is 900 in the beginning and grows by 350 people each year for 20 years. B. The pop...

A: B - given is the population is 900 in the beginning and decreases by 12% each year for 5 years.

Q: ds V9-s 9-52 + C 95 9s + C A. C. B. D. + C 95 69/

A: Given: I=∫dss29-s2   ...1   We know that, the trigonometric identities. 1). 1sinx=cscx 2). sin2x+cos...

Q: Scos x vsin x dx (sin x)i-(sinx) +C (sin x)i +(sinx)+c c. (sinx)- (sinx) + C (sinx)i +(sinx)+c A. B....

A: ∫cos3xsinxdx  

Q: (a) Express sin(2 cos-1x) in an algebraic form. Furthermore, sketch this function and find its domai...

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Q: x² – 49 .2 if x + -7 f(x) : x +7 -12 if x = -7

A: