Find the derivative of the following functions using limits. 1. f(x)= 3x² + 4x-5 2. f(x)=x³2x²+x-3 3. f(x)=(x-1)²

Q: Use implicit differentiation to determine dy dx dy given the equation ey² + cos(x) = e. dx

A: Topic-implicit differentiation We are given, ex·y2+cos(x)=eywe know thatddx(u·v)=uv'+vu'ddxxn=nxn-1

Q: lim (1+1)* 148

A: Please see the below picture for detailed solution.

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A: Given query is to find profit and marginal profit.

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A: Graph:-

Q: Find the critical point(s) of the function f(x, y) = x² + y² − 40xy. Enter your answer as an ordered…

A: To find the critical points of the function fx, y=x4+y4-40xy.

Q: Find a function r(t) that describes the line passing through P(9,7,2) and Q(3,2,9). r(t) = (-6t+9,,…

A: See this solution in below.

Q: Consider the following. 3x³ - 27x² + 5 y = (a) Find the critical values of the function. (Enter your…

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Q: Question Let h(x) = f(g(x)). If g(5) = −3, g'(5) = −4, f(-3) −4, ƒ(−3) = −1, and f'(-3) = -5, find…

A: Let hx=fgxIf g5=-3, g'5=-4, f-3=-1, and, f'-3=-5, then to find h'5.

Q: 4 Find the derivative of f(x) = x¹ log7(x + 4.5). f'(x) =

A: Given that f(x)=x4log7(x+4.5) Differentiating with respect to x…

Q: Consider the function: f(x)=7x+1 Step 2 of 2 : Find the value of f(a+5)

A: Consider the function: f(x)=7x+1Step 2 of 2 :   Find the value of f(a+5).

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A: Concept: The slope of a function can be found in its first derivative. The slope of the curve grows…

Q: an+1 Use to show that the sequence given by an (a) (c) Strictly increasing (b) Strictly decreasing…

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Q: 2ydx + (x x³y³) dy = 0

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Q: Let f(x)=10-th (cosh (x)) Find f'(In 3).

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Q: Assume that the water coming from the end of a horizontal pipe 25 ft above the ground is parabolic…

A: Assume that the water coming from the end of a horizontal pipe 25 ft above the ground is parabolic…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. IL VE - dy dx

A: ∫141 ∫x8x xydydx

Q: 1. Each of the following integrals can be found by making a substitution u for part of the…

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Q: Given that f(x) (a) (f + g)(3)= (b) (f - g)(3)= (c) (fg)(3)= (d) (-) (3)-[ = x² - 7x and g(x) = x +…

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Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at…

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Q: Let f(x) = ln(x² + 4x + 9) In f'(x) =

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Q: Consider the function below. (Round the answers to two decimal places. If you need to use - or∞,…

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Q: The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t, where…

A: Given query is to find the population after 6 days.

Q: Find the critical point(s) of the function f(x, y) = x¹ +y¹ − 40xy. Enter your answer as an ordered…

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Q: Let S be the solid inside the sphere x2+y2+(z-3)2 = 9 and the below the cone x2+y2 = z2.   Setup…

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Q: Write an equation describing the relationship of the given variables. y varies inversely as the…

A: y varies inversely as the cube root of x and when x=125, y=3.

Q: on 5 Given original function AND x-1 x+2 3 (x+2)² f(x) = where f'=- Ari nolbar, press ALT+F10 (PC)…

A: We have given  f(x)=x-1x+2 and f'(x)= 1(x+2)2 Find interval of increasing and decreasing.

Q: If g(x) = cos(x) then g'(x) = g'(4) = (round to 3 decimal places)

A: If gx=cosx, then to find g'x and g'4.

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Q: Find the arc length of f(x)=ln|x| over [1,3]. Round answer to two decimal places

A: We will find the required arc length.

Q: Question Find the derivative of the function f(x) = ln Select the correct answer below: 3 Xx O f'(x)…

A: The given function is; f(x)= ln[x3(2x+1)/(x2-3)].

Q: Consider the function f(x) — ² 10x + 29. What is the absolute minimum of f(x) on the interval [0,…

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Q: + 1, the x-axis, x = -1, and x = 2. Use the Define R as the region that is bounded by the graph of…

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Q: 1. Among 200 people, 150 either swim or jog or both. If 85 swim and 60 swim and jog, how many jog?

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Q: A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After…

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Q: y" + y = 2, y(0) = 4, y' (0) = 3 (A) y = 2 sint + 3 cos

A: given y'' + y = 2 D2y + y = 2(D2 + 1 ) = 2 for complementary solution D2 + 1 =0D = ±iD = 0…

Q: Evaluate the integral. [²3 0 x In (3x) 4 dx

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Q: Exercise 5 Determine a value of 8>0, that satisfies statement: If 0 < x - 3|<8, then f (x) +1|<1. YA…

A: We determine the equation representing f(x) and proceed further. Equation of line passing through…

Q: Given 2y-√x-z+2√-5y-4z = -5, calculate Provide your answer below: || dz dx

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. 2 48x S (x-9)(x+3)²…

A: Given, ∫48x2x-9x+32dx

Q: the third Taylor polynomial for f(x) = expanded abc= 3(x)=7-7(x-1)-14(x-1)²-7(x-1)³…

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Q: 1. [e²y ycos (xy)] dx + [2xe²y xcos (xy) + 2y] dy = = = 0

A: According to guidelines I can only solve first question ,rest can be reposted.

Q: Laplace transforms. y' + 9y = 0, y(0) = -1

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Q: 1. Integrate each of the following. a. f 3x²e³x dx b. fxco. xcos(4x)dx

A: (a) Given that ∫3x2e3xdx

Q: Could you find A,B,C,D

A: Given, f(x)=a(x+b)(x+c)(x+b)(x+d)

Q: dy Given x²y + xy = 3, use implicit differentiation to find da da dy da da da = = 2xy + 1 x² + x 2xy…

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