y y = f(x)

Q: Find two positive numbers whose sum is 7 and the product of the cube of one number and the exponenti...

A:  

Q: Find the most general antiderivative of each of the following functions  f(x) = x n   , n not equal ...

A: If F is the antiderivative of f then the most general antiderivative of f is = F(x)  + C  where C is...

Q: Determine the differential of the function y=x3−3x2+4x at the point x0=1 when dx=0,1.

A:  

Q: calculate the integral.

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Q: compute the definite integral.

A: We integrate by parts  

Q: Find two positive numbers whose sum is 32 and the sum of their square roots is maximum.

A: Let the two numbers are x and (32-x) So the sum of their square roots is:  

Q: denote the balance at time t (years) of an annuity that earns 5% interest continuouslycompounded and...

A:

Q: 2- Please I want solution of this question. Thanks   Z = 8

A: Let the number is x So, 4 times sum of x and 9 is =4(x+9) the subtraction of six times x and Z is = ...

Q: Does the following improper integral converge? If yes, towards what number?

A: To determine the converges and divergence of the integral.

Q: 5a - Please I want solution of this question. Thanks   ID digits = 48

A:

Q: Find the most general antiderivative of the function.(Check your answer by differentiation.)   f ( x...

A: To find the antiderivative of f(x), we integrate it C= integrating constant  

Q: Find the points of intersection of the graphs of the equations                             x2 + y2 =...

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Q: Find the global maximum and minimum of the function on the given interval:f(x)=cos2x−2sinx,x∈[0,2π].

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Q: I need help with parts g, h and I

A: (g)

Q: I need help with a, b and c please

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Q: Find all values of the parameter a, for which the function f(x)=x3−6x2+ax is strictly increasing in ...

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Q: COS X dx sin? x – 3 sin x + 2

A: Consider the given indefinite integral

Q: Find R'(0), where x - 3x' + 5x 1+ 3x' + 6x + 9x° R(x) Hint: Instead of finding R'(x) first, let f(x)...

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Q: Find dy/dx by implicit differentiation   2x3 +x2y  -xy3  = 2

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Q: Find a function f such that f ' (x ) = x 3 and the line x + y =0 is tangent to the graph of f

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Q: (8x-12)(4x² – 12x)ª dx

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Q: 1. Find the following products of complex numbers a. (2 + 3i)(4 – 2i) c. (-1 – 2i)(2 + i) b. (2 – i)...

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Q: Find dy/dx by implicit differentiation   y Cos x = x2 +y2

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Q: Find the linearizations L(x, y, z) of the function at the given points. ƒ(x, y, z) = xy + yz + xz at...

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Q: In Exercises 7–12, one of sin x, cos x, and tan x is given. Find the other two if x lies in the spec...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: What is Gradient Matrix ? Illustrate.

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Q: If A and B are n × n diagonal matrices, show that AB = BA.

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Q: Show that a fraction r = a/ b in lowest terms has a finite decimalexpansion if and only ifb = 2n5m f...

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Q: Please apply u-subsitution.

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Q: Find the critical points of the function f(x)=sin2x−cosx on the interval (0,2π).

A: For critical points, first find the derivative of the function and equate it to zero.

Q: A particle is moving along the x-axis so that its position at time t≥0 is given by the equation x(t)...

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Q: Please see attached. Thank you

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Q: dy is let y = cos(In(cos(x))), then da

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Find the limit

A: We will solve this by substitution We plug x=1  

Q: Divide numerator and denominator by the highest power of x in thedenominator and proceed from there....

A: We divide the numerator and denominator by x2  

Q: Sketch the graph of y = f(x + 2) - 1, where f(x) = x 2 for -2 < X < 2.

A: From the given function:

Q: x³ex² dx (x²+1)2

A:

Q: Using the second derivative test, find the local extrema of the function f(x)=x3−9x2+24x−7.

A: We find the first and the second derivative using the power rule   

Q: lip = (x+y+1)? – (r + y – 1)? subject to y(0) = dr %3D dy_I- y - 1 dr I+y+3

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Q: 5d - Please I want solution of this question. Thanks   Z = 8

A: a) Answer(i): Acute angle

Q: Describe the set of real numbers satisfying Ix - 31 = Ix - 21 + 1 as a half-infinite interval.

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Q: 1- Please I want solution of this question. Thanks

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Q: Find the number whose sum with its reciprocal is a minimum.

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Q: Find the derivative with respect to t for the function y = 2/t.

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Q: What does ∆2xk equal?

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Q: ƒ(g(1))

A: From the table we can see at x =1 g(1) = -1

Q: Find the local (relative) extrema of the functionf(x)=−x2+4x−3.

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Q: Test for symmetry with respect to each axis and to the origin y = x /(x2 + 1)

A: To test symmetry of a function about x axis, replace y with -y in the given function y axis, replac...

Q: Estimate the slope of the graph at the points (x1, y1) and (x2, y2)

A: At (x1, y1) the tangent is horizontal. The slope of a horizontal line is 0. So the slope of the grap...

Q: Find the evolute of the parabola y=x2.

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.