If y =le In(1+x) d²y dy xe* show that (x+1)² dx - dx

Q: Find the equation of the tangent line to the function f(x) -x2 – 4x + 4 at the point where x = -2. =...

A: Answer is- Option 3 is correct Explanation is given below...

Q: if 20 000 is invested at an interest rate of 2 per year, compounded semiannually, find the value of ...

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Q: Graph the function.   f(x)= −x+3 if x<2 2x−3 if x≥2

A: Given,            f(x) = -x + 3    if x < 22x - 3    if x ≥ 2

Q: Help with steps to solve

A: Given :  hx = ∫1x8t3 + 2tdt

Q: If √x+√y=10 and y(1)=81, find y'(1)by implicit differentiation. Enter exact values. y'(1)=

A: Given : x + y = 10

Q: dy Find of the equation x'y +4y=3x dx %3D

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Q: Differentiate the function. 1 9(x) = - (2x3 + 3x + 5)3/4 g'(x) =

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Q: Evaluate det(A) by a cofactor expansion along a row or column of your choice. 3 3 5 2 0 -2 (a) A= 4 ...

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Q: Find​ s(t), where​ s(t) represents the position​ function, v(t) represents the velocity​ function, a...

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Q: If f(t) is measured in dollars per year and t is measured in years, what are the units of f(t) dt? y...

A: f(t) is measured in dollars per year

Q: What interest rate (compounded continuously) is earned by an investment that triples in 6 years? A r...

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Q: Please graph the following function, labelling any maxima, minima, or points of inflection. y=-x'+6x...

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Q: Grandparents plan to open an account on their grandchild's birthday and contribute each month until ...

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Q: Evaluate the expression without using a calculator. IT 2 sin tan + csc 4 3

A: Given: An expression sinπ3tanπ6+cscπ42

Q: Find the equation of the tangent line of f (x)= x² In x at x=1.

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Q: Let f(X)=2x3+3x2+36x over the closed interval (-3,5) That is the smallest critical point

A: Given: f(x) = 2x3+3x2+36x  over the interval (-3, 5). To find: The critical points of the given func...

Q: Differentiate and simplify. f(x)=Je* +In (x² +4)

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Q: Find the area of the region enclosed by the curves y=x2 and y= 6x-x2.  Show the area on the graph. P...

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Q: esin 2x + sin(e2"). Find dy Show your work. dæ Let y =

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Q: f(x) = e*, approximate f(0.8)

A: Given: f(x)=ex To find: The degree of the maclurin polynomial.

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 1) dt

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Q: 3-2x2 Find the derivative of y =- and simplify your answer. 5x +2

A: Given: y=3-2x25x2+2  To find: Derivative of the given function.

Q: Need help breaking down steps to solve

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Q: If f' (4) = –4, and g(x) = 5f(x), what is g' (4)? Do not include "g'(4) =" in your answer. For examp...

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Q: Evaluate the expression without using a calculator. sin 30° cos 60° + sin 60° cos 30°

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Q: 25 7 24 sin(0) = cos(0) = tan(0) = csc(0) sec(0) = cot(0) = II

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Q: Find the equivalent expression: cot e+ 1 Select one: O a. tan esec²e O b. cot² @sec² e O c. cot? @co...

A: Given expression is , cot2ϑ+1 Use trigonometrical identity cotθ=1tanθ Now substitute 1tanθ for cotθ ...

Q: 2. (a) Suppose that f is a differentiable function such that |f'(x)| < c for every x. Show that for ...

A: To Prove: a. If f is a differentiable function such that f'(x)≤c for every x.Then for any real numbe...

Q: Evaluate the expression without using a calculator. sin " + cos 4 4

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Q: Need help with laying out steps to solve

A: Given: f(x)=x2,  [0,4]

Q: Find the area of the region bounded by graphs of f(x) = x³, x = -1, x = 2, and y = 0 %3D a) Analytic...

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Q: pls its an hard quiz

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Q: Find the equation of the tangent line to the function f(x) = 2x° + 3x2 + 4x +2 at the point where x ...

A: Given : fx = 2x3 + 3x2 + 4x + 2

Q: ​D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​ item...

A: Given D(x)=(x-6)2 S(x)=x2+2x+22 (a) Equilibrium point is evaluated as follows. D(x)=S(x) (x-6)2=x2+2...

Q: If f' (2) = 3, and g(x) = 9f(x), what is g' (2)? %3D Do not include "g' (2) =" in your answer. For e...

A: Given that g(x)=9f(x) Applying differentiation with respect to x on both sides Then g'(x)=9f'(x)

Q: I need help with this question.

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Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the function...

A: Given  Marginal function C'x=-425x+58 for x≤350 cost for 180 dresses are $7848 cost of producing 181...

Q: 3 Determine the intervals for which the function f(x) = x° + 18x +2, is decreasing.

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Q: dy -x +e* + dx 1 and y(1) = 0, which of the following would be the constant of integration of the fu...

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Q: Use logarithmic differentiation to find the derivative of the function. y = xIn(x)

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Q: Find these on the graph

A: The figure given in the problem represents the graph of the function y=f(x). The region under the cu...

Q: Find the initial value a, growth/decay factor b, and growth/decay rate r for the following exponenti...

A: Known fact: The exponential function is of the form y=a bt  or  y=a 1+rt where a is initial value, b...

Q: A piece of wire of length L is to be cut into two pieces, one piece to form a square and the other p...

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: