Find exactly the vector oppositely directed to v = (3) and half the length of v.

Q: Given that 2i is a zero of m, write the polynomial in factored form as a product of linear factors:…

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Q: Question #4 - Find the derivatives of the following functions A) f(x) = LN(*²-7) 2x

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Q: Please show your answer to 4 decimal places. Find the direction in which the maximum rate of change…

A: We need to find out the direction in which the maximum rate of change occurs for the given function…

Q: The temperature, T in degrees, over a twenty four hour period at a particular weather station is…

A: Here we have to observe the graph.

Q: 8. A fast food restaurant determines that the cost C and revenue R for x hamburgers an be…

A: We need to find out the profit function and also the critical point and maximum or minimum at that…

Q: 3π (a) Write out the degree 2 Taylor polynomial T₂(x) for f(x)=sin (2x) about center a=³ 8 You may…

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

Q: Consider the function f(x) = 12x5 + 60x¹ - 100x³ +2. f(x) has inflection points at (reading from…

A: function

Q: (a) by interpreting it in terms of areas. Show the graph! (b) [VI6=240 f(x- (x + √81-x²) dx

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Q: Suppose f is continuous on [0,13] and differentiable on (0,13). If f(0)=3 and f′(x)≥9 for all…

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Q: Determine the area of the region bounded by y = x³, y = -x³ + 1 and the y-axis

A: We first need to plot the area ÷ Shaded region is our area to be determined.

Q: 30) Emily has a gift certificate for $10 to use at an online store. She can purchase songs for $1…

A: Given: Emily has a gift certificate for $10 to use at an onlinestore. She can purchase songs for $1…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(zy)…

A: To find the direction of the maximum rate of change of the function f(x,y) = 5x sin(xy) at the point…

Q: Find the Taylor Series for f(x) = xe²¹ at x = 1.

A: Taylor series of function fx at a is defined as:  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+… Here,…

Q: Determine whether the given series converges or diverges. If it converges, find its sum. (Express…

A: Given series:- ∑k=1∞sin1k+1-sin1k+2

Q: Answer the following questions for the function f(x)=x√√x²+4 defined on the interval -5 ≤ x ≤ 4.…

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

Q: Verify that the function is a solution of the initial value problem. (a) y = x²(1 + Inx): y" =…

A: Given:y=x23+x-1   We are required to find: If y is the solution of the initial value problem…

Q: Suppose R '(1) = 2. (a) If f(x) = R(6x), find f'(2) F' (1) = f (b) If g(x) = R(x + 5), find g'(-4).…

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Q: Determine if the following series is convergent or divergent. η2 * 7n Σ (n + 1)! n=0

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Q: Find and classify the critical points of z=(x² - 7x) (y² – 6y). Local maximums: Local minimums:…

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Q: ntegrate the following function with respect to x using partial fractions: 2x - 3 x2 – 5+6 and hence…

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Q: Find the absolute maxima for the function: f(x) = 3 Enter the exact answers.

A: We have  fx=3x+sin3xx∈0,2π

Q: 11) An elliptical riding path is to be built on a rectangular piece of property that measures 6 mi…

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Q: C(x)=2.2x+4,000 and revenues are represented by R(x)=9.4x, which even point?

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Q: 9. Suppose P = spending s (in a. Is the profi $41,000? R $2000, etc.

A: Given function P = -0.1s3 + 6s2 + 400where P = profit s = spending on advertising

Q: 4. Evaluate the following limits. 3x+1 a. lim x⇒-2 2-x b. lim x³+27 X-3 x+3

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: y = g(x) on [-3, 4] is given by the following curve, which is composed of two line segments and a…

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Q: The doubling period of a bacterial population is 20 minutes. At time t = 90 minutes, the bacterial…

A: The doubling period of a bacterial population is the time it takes for the population to double in…

Q: Find the Tim X 70 XttanX Sin X limit.

A: We have limx→0x+tanxsinx L'hospital Rule for limx→afxgx=limx→af'xg'x if its 00, ∞∞ etc forms

Q: A water tank is created by revolving the graph y=1/x about the y-axis, with the v(h) = √ ^ 72 dy.…

A: A water tank is created by revolving the graph y=1x about the y-axis with the bottom of tank at y=1.…

Q: Consider the function f(x)=x^3e^8x,−3≤x≤1 The absolute maximum value is = and this occurs at x…

A: Here we have to find the absolute extrema.

Q: Let f(v) be the gas consumption in liters/km of a car traveling at velocity v km/hr. In addition,…

A: f(v) be the gas consumption of a car travelling at velocity v km/hr.f(60)=0.05f'(60)=0.0005

Q: Z = XY X-Y Find the partial derivative of Zxy= = Ans: Zxy: - 2xy (x-Y)³

A: Given: z=xyx-yWe need find zxy.

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

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Q: Factor out the negative greatest common factor, -5a-10. Drag pencil to correct answer.

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Q: so i dont understand whats the answer

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Q: -8 -7 -6 -5 -4 -3 -2 -1 8 7 6- 5 4 3 2 6 7 8 1 2 3 4 5 5 6 ind the area inside the circle x² + y² =…

A: We have to find the area according to the given information

Q: 5. Compute the derivative of y = (4x + 1)³x. Write an equation of the tangent line to the graph at…

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Q: When a particle is located a distance z meter from the origin, a force of f(x)=3z² + 4z -newtons…

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Q: A plane is currently 4000 km from its destination. 1.75 hours later, it is 3300 km from its…

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Q: The total cost (in hundreds of dollars) to produce x units of perfume is C(x) (a) Find the average…

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Q: Given h(x) tangent line to h(x) at x = -1? = -2x³ +=; x (A) y - 1= 5(x - 1) (B) y-3-7(x + 1) (C) y -…

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Q: = = 2.3219andlog, y = 2.8074. Given log, a Evaluate log, a

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Q: Question #2 - What is the interest rate of an investment is it takes 5 years to double my…

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Q: Find the points at which y=f(x)=2x−ln(4x)has a global maximum, a global minimum, and a local,…

A: Given function y = 2x-ln(4x). Where x€[1,2.8] We have to find the global maxima , global minima and…

Q: A hemispherical tank, 10 ft in diameter is full of liquid (density: 40 lb/ft³). Find the work…

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Q: The velocity, v m/s, of a particle at time t seconds is given by v = t³ - 3t² + 4t - 4 Show that the…

A: Given query is to show that acceleration can not be less than 1.

Q: An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds…

A: Here is the solution:

Q: Find f'(x) if f(x) = x cos (x²) dy inddx _y=²csc(√x) b) Find

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Q: Find the limit of the sequence. {√3,√3√3, √3√3√3, ...}

A: 0⁰Pp⁰