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Q: If x2 + y? = 36 and dx/dt = 3, find dyldt when y is positive and (a) x = 0: dyldt = (b) x = 1: dyldt...

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Q: Explain how to use the graph of f(x) = 2x to obtain the graph of g(x) = log2 x.

A: given: the function f(x)=2x the other function is g(x)=log2x. let the given function f(x)=2x as y. t...

Q: Please show the solution on how to compute for the intercepts and local extrema of y= sin2(x)-2cos(x...

A: Given: The function y=sin2x-2cosx To find: x and y intercept and local extrema of given function.

Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule. fx=ex+24f'x=ddxex+24f'x=ddx+2ex+...

Q: Solve Step 2 beyond

A: It is already given step 1 as shown below.

Q: Find the general solution to the given differential equation. (Use C for the constant of integration...

A: Given differential equation is dydx=x3y

Q: Find a formula for the nth term of the sequence:

A: We have to find the formula for nth term of the sequence: 51,82,116,1424,17120...... Here we have to...

Q: Please very soon full explanation

A: Here, the objective is to find the following: a) 3, 3, 3, 3, .... as its second difference. b)1, 2, ...

Q: Match the equation 4x2 + y2 = 4 with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and...

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Q: 13.5 #7 Question 7 please explain every steps , even the simple steps . I get confused

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Q: A 15 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how ...

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Q: Find the curvature of the curve r(t) = a cos ωti + b sin ωtj .

A: Given vector is r(t)=acos ωti+b sin ωtj . Compute the derivatives. r'(t)=acos ωti+b sin ωtj'=-aωsinω...

Q: (2x 1) (x+5) 3) Let R(x)= %3D (3-x) (x+4)2 3a) Determine the intercepts of R. 3b) Fin the equations ...

A: Given: Rx=2x-1x+5 3-xx+42

Q: The boundary of a lamina consists of the semicircles y = V4 - x2 and y = V 36 - x2 together with the...

A: The semicircles are y=4-x2 and y=36-x2

Q: Solve the differential eqution y'-y=7e^x

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Q: A kite 100ft above the ground moves horizontally at a speed of 8ft/s. At what rate is the angle betw...

A: Given Kite flies at the height of 100ft horizontal speed of kite is 8ft/s To find the rate of angle...

Q: Use the shell method to find the volume of the solid generated by revolving the plane region about t...

A: Given y = 7x − x2 y = 0 about line x = 9

Q: Show the solution on how to compute for the point of inflection and concavity of y= sin2(x)-2cos(x) ...

A: Consider the following equation: y=sin2x-2cosx Differentiate y with respect to x: y'=2sinxcosx+2sinx...

Q: (a)(1,−2) (b)(−1/3,−2/3) (c)(−2,1) (d)(0,0)

A: Consider the curve x=1-3t2,y=t-3t2If the tangent at point (1-3t2,t-3t2) inclined at an angle θto the...

Q: Find the inverse of f(x) = x3 + 1.

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Q: A spring in equilibrium has length 1 meter. If ittakes 40 joules (i.e., kg-msec2 ) of work to stretc...

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Q: Give the center and radius of the circle described by the equation (x + 2)2 + (y + 2)2 = 4 and graph...

A: the given equation of the circle is x+22+y+22=4 the equation of the circle can be written as: x+22+y...

Q: ng to his calculations reds of dollars) t yea Ets 8)

A: Here P(t)=t3-16t2+25t+50 , (0≤t≤8) The inflection point is the point where F''(t)=0 Then at ...

Q: Use logarithmic differentiation to find the derivative of the function. y = square root of ((x-5)/(...

A: Given: y=(x-5)x6+4y=(x-5)x6+412 While applying logarithmic differentiation , we take ln on both side...

Q: consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b sin(ωt)...

A: Consider a particle moving on a circular path of radius b given as, rt=bcosωti+bsinωtj Where ω=dudt ...

Q: The following limit represents the derivative of a function, f, at some number a: lim h->0 sin(1...

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Q: Find an equation of the tangent to the curve at the given point by both eliminating the parameter an...

A: Given parametric curve x=2+lnt .....1y=t2+2 .....2 and Point P=2,3

Q: Here we will study the function f(x) = xe^-x , where x ∈ [0, 10] Determine where the function is...

A: Given fx=xe-x ; x∈0 ,10

Q: the left and right page of an open bookare two consecutive intergers whose sum is 253?

A: let the page numbers are left page n and right page is (n+1)

Q: Find the dimensions that give the largest area for the rectangle shown in the figure. Its base is on...

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Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through...

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2) y-5=14(x-2)4y...

Q: A rectangle has one side of 10 cm. How fast is the area of the rectangle changing at the instant whe...

A: Given that: Let the one side of rectangle is (a) = 10 cm and the other side of rectangle is (b)= 18 ...

Q: Question attached

A: Here we use the formula of power rule of derivative.

Q: (a)f is differentiable at x = 0 (b)h is differentiable at x = 0 (c) foh is differentiable at x = ...

A: To verify f is differentiable at x=0, calculate limh→0fx+h-fxh. limh→0f0+h-f0h=limh→0fh-0h=limh→0h...

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =...

A: Concept: The calculus helps in understanding the changes between values that are related by a functi...

Q: Find the derivative of the function.

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Q: f(x) = √x + 2 a. Find an equation for f -1(x).b. Graph f and f -1 in the same rectangular coordinate...

A: (a) The function f(x)=x+2. To find the inverse of the function, first replace x with y and obtain t...

Q: dy/dx=x squre root of y for y doesnt equal 0 Solve the differential equation

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Q: The percentage of adult height attained by a girl who is x years old can be modeled by f(x) = 62 + 3...

A: Given: The percentage of adult height attained by a girl who is x years old can be modeled by fx=62+...

Q: Consider the following. f(x) = 3x√(4-x2), [-2, 2]a. Use a computer algebra system to differentiate t...

A: Consider the given function, fx=3x4-x2 used differentiation formulas, ddxxn=nxn-1ddxconstant=0ddxCfx...