Let f(x) = 3x² + 12x − 5. Using the definition of derivative, f'(x) = lim h→0 enter the expression needed to find the derivative at x = 4. f'(x) = lim h→0 f(x+h)-f(x) h After evaluating this limit, we see that f'(x) =

Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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Q: QY == Given f(x) = (hog|(x), and f(1) = 2/'`(1) 9 (²) = g(1) f = - Find (gof) (1) in simplest form :

A: Given- Given fx = h∘gx, and f1 = 2f'1 = g1 = -g'1 To find- Find g∘f'1 in simplest form.

Q: Find the DE of the following by eliminating arbitrary constants. Reduce your final answer in…

A: The given equation is; x4-4xy=c.

Q: (a) Use the information in the table to determine the average rate of change on the intervals i. day…

A: We have to answer there subparts in this question and they are related to rate change.

Q: Deposits of $850 per month are made into an investment account. The interest rate is 6.5% per annum…

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Q: B.    Find the DE of each of the following by eliminating arbitrary constants               1.…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Find the DE of a family of circles with center at (1, -2). Hint: Equation of circle with center…

A: Let's find diffrential equation.

Q: Q4) Find the volume of the solid generated by revolving region bounded by curve y=√x and the line…

A: We will find the volume of the solid generated by revolving the curve y= sqrt x and the line x=4…

Q: Prob 2 Use the Direct substitution rule and justify why you can use it to evaluate Лет 2-2 ln x + ex…

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Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

A: We can find the answer as below.

Q: √ ¹ (1+√x)3 √x - dx

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Q: Consider the following function and graph. f(x) = 1 x + 3 (b) lim f(x) x-3+ -4 -2 X y 4 2 -2 -4 2…

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Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

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Q: 2. Let f(x)=x²-3x+7. Answer the following: a) f(4) = c) f(1/2) = b) f(-3) = d) f(t+2) =

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

Q: 19 tenths x ____ te

A: Given: 0.9x0.9

Q: if f(x) = x + 5* . find the derivative of this function f'(x) A. f'(x) = 5* In 5 B. f'(x) = -1 + 5*…

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Q: Prove the identity. (secx-1)² secx-1 tan²x secx + 1 Note that each Statement must be based on a Rule…

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Q: area

A: Given,r   =   cos ( 2 θ ) ,     - π/4 ≤   θ ≤   π/4 Given is a polar curve.

Q: I'm 4-√3x + 1 2=75 2²²-7x+10

A: We can solve this as follows:

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the fun f(x) =…

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Q: Obtain the differential equations of the following by ELIMINATING ARBITRARY CONSTANTS. 2. y(x) = ₂x…

A: We have 2 arbitrary constants so we differentiate the given equation 2 times to find it's…

Q: (1+x²-1) y = tan²¹ / √₁+x²

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim 7 cot(x) X-R

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Q: Calculate C 4 (x+y+z

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Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

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Q: Find the percent of increase or decrease to the nearest whole percent.  $8.00; $10.00

A: Percent of increase of a value= (new value - old value)*100/old value

Q: 2 1 1 -1 -2 2 3 4 5 6 2 7 { a The graph above shows the base of an object. Compute the exact value…

A: Concept: The Area of the half disk is given by A=π2y2 The volume of the region is given by V=∫abAdx…

Q: Find the length of the curve x = 5-t, for 1 < t < 2. y = 3-t, z = 3t - 5,

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Q: Change these fractions into decimals. Express each answer to three significant figures. Be sure to…

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Q: Find the DE of each of the following by eliminating arbitrary constants. Reduce your final answer in…

A: Concept: Differential equation: Any equation with one or more terms and one or more derivatives of…

Q: 2. Solve the Differential Equations. (y² - xy )dx + x² dy HO

A: To solve the given differential equation.

Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: Find the Differential Equation to the given Solution x sin y - xy² = c

A: To find the differential equation corresponding to given function.

Q: Eliminate the arbitrary constant. y=Ax² + Bx³ 7xy "-x²y + 15y = 0 A (В) B (C) D x²y-7xy "+ 15y = 0…

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Q: lim x→2 f(x), where f(x) =    10  −  2x    if x < 2 x2  −  x    if x ≥ 2

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Q: What is the image of the point (-7,9) after a rotation of 270 counterclockwise about the origin

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Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2 Ans: 2xy" - 4yy"…

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Q: whats the imaginary part 2 − 4i

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Q: Show that y = In (x) is a solution of xy" + y² = 0.

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Q: Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has been cut…

A: Given- Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has…

Q: Find the DE of the following by eliminating arbitrary constants. Reduce your final answer in…

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Q: (a) lim f(x) (b) lim f(x) x-2+ (c) lim f(x) x-2 (d) f(2) (e) lim f(x) X-4 (F) (4) Need Help? Read It…

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Q: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: 1. Use the tables to find the z transforms of the following a. 6 b. 2 c. e 2n

A: As we know that, L{1} = zz-1

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: Here, the given sequence is: 2-8, 3-9,4-10,...

Q: The profit function of a certain firm is f(x) = -6x² + 1188x - 1200, where x denotes units of…

A: The profit function is fx=-6x2+1188x-1200 Here, x is the number of units produced. Part a We need to…

Q: The table gives the population of a country, in millions, for the years 1900-2010. Year P = 1900…

A: NOTE: Refresh your page if you can't see any equations. . x=number of years after 1990 y=population…

Q: MARKETING A company makes two products, A and B. The manager estimates that if x% of the total…

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Q: Write the radical expression using exponents. 9   62 9 power square root 6 to the 2 power

A: Given expression,  9 power square root 6 to the 2 power  to be written as a radical expression…

Q: A graphing calculator is recommended. A bacteria culture starts with 900 bacteria and doubles in…

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