1. Differentiate the following functions f(x)= f(x) = x² cos(x) a. b. f(x) = sin²(5x) c. f(x) = sinx cosx

Q: Given f(x) = = 3x + 7 √9x² A) Find lim f(x) ° x48 5 B) Find lim f(x) o x118 "

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Q: Solve 4x cos(3x) dx using Integration by Parts. 4x 3 + sin 3x + 4 cos 3x + c

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Q: Evaluate the integral. म (3ex+ 5 sin(x)) dx

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Q: Problems In each of Problems 1 through 11: a. Seek power series solutions of the given differential…

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Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: 1. For the function ƒ(x) = -x² + 4x + 1, (a) Calculate the average rate of change of the function at…

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Q: Consider the following. dz Find by using the chain rule. (Enter your answer in terms of t.) dt dz dt…

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Q: The following graph of the function f satisfies limf(x) = -1. In the following exercises, determine…

A: Given :- The graph of the function f satisfies with limx→3f(x)=-1 To find :- A value of δ>0 That…

Q: Find a quadratic equation with the given roots. Write your answers in the form Ax2 + Bx + C = 0.…

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Q: The process of synthetic division applies equally well when some or all of the coefficients are…

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Q: Compute the area of the surface parametrizes by r(u, v) = (u cos v,u sin v, 1-u²), where 0 ≤u ≤ 1,0…

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Q: 4. Determine the 75th derivative of each of the following functions. f(x) = 3 cos 2x b)

A: given function is f(x)=3cos(2x) we know d dx(cos(ax))=-asin(ax)  and d dx(sin(ax))=acos(ax)

Q: Evaluate the double integral changing to polar coordinates. ¹/1₁ (² (2x - y) dA, where R is the…

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Q: a) lim (-2x¹) = 8118 ) lim (-2x¹) = xx ) lim -√x = 118

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Q: The following graph of the function f satisfies lim value of 8 >0 such that the precise definition…

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Q: 10Let C be the curve defined by the parametric equations x = t^3 - 3t + 2 and y = 3t^2 -9. a.…

A: As per guidelines we support only Frist three part of the questions.kindly repost in next request.

Q: Discuss the differentiability of f(x)=√x²-x 1₁

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Q: Compute the following. Enter your answer as a fraction. 27 ** (-+ ) *- dx = 2

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Q: lim Δx→0 3 1 x + Δx Δε 1 της X

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Q: First make a substitution and then use integration by parts to evaluate the integral Se 6x5ex² da…

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Q: √2 cos 0 + √2 sin 6, find the Cartesian equation of the tangent line v Given the polar curve r = to…

A: We need to find equation of tangent line.

Q: Determine whether the three points P = (-5, -4,-3), Q = (-8,-10, -12), R = (-11, -15, -21) are…

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Q: 8. Find 7. || = 23 55° || = 31

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Q: Use interval notation to indicate the domain of x + 1 f(x) x² + 10x + 25 = Answer: * E Note: Input…

A: The given function is fx=x+1x2+10x+25

Q: /n³ + 1 n=1 3n³ + 4n² + 2 00 EXAMPLE2 Σ Since an is an algebraic function of n, we compare the given…

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Q: Use the limit comparison test to determine whether an = n=12 an lim = lim n→∞ bn n-x n=12 (a) Choose…

A: We have to to Check the convergence of given series.

Q: Find equations of the normal and osculating planes of the curve of intersection of the parabolic…

A: The curve of intersection of the parabolic cylinders x = y2 and z = x2 at the point (1, 1, 1). Find…

Q: Suppose f(x) = 2 + 8x². Determine, in a simplified form, each of the following: (a) f(a) = (b)…

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Q: The demand function for Cheap Chips Corp. device model OFD580 is given by d(g) = 252.7 -0.4q² while…

A: At the Equilibrium point the demand function equals the supply function. Suppose the Equilibrium…

Q: 5. Find f'(x) if f(x) = √4sin²x +9 cos²x. Solution: U= du dx B) Implicit Differentiation Example:…

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Q: Use the chain rule to find dw dt = dw dt w = In (√x² + y² + z²), x = 8 sin(t), y = 7 cos(t), z = 2…

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Q: I have a few questions: How did you get from (sin2(x)+sin(x)+5sin(x)+5)/(sin2(x)-12) to…

A: Given:f(x)g(x)=sin2x + 6sinx + 5sin2x - 12   Basic information: 1. x2 + a+bx +ab =x+ax+b2.…

Q: 7. Given = [-4,4,4] and ✓ = [-5,6, 2] find a. 2ū + 4v b. c. u x d. lul V V

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Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 26 cm…

A: Volume of the cylinder = πr2h where r is the radius and h is the height of the cylinder.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1200 feet apart. As the…

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Q: Second derivative of f(x) =2^x/x

A: To find the second derivative of the following function. fx=2xx

Q: Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of…

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Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

Q: Find the rate of change of ƒ (x, y, z) = 6xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: 19. an - (₂)

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Q: 6) The velocity of an object on the interval 0 ≤ t ≤ 10 is shown in the graph below. If v(t) is…

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Q: 12. Practice similar Help me with this Use the Integral Test to determine whether the infinite…

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Q: Use the equations to find дz Әх az ду - дz Әх əz Әх = and ƏF Әх ƏF əz and дz ду əz ду x2 - y2 + z² -…

A: x2-y2+z2-6z=7∂z∂x=-∂F∂x∂F∂z∂z∂y=-∂F∂y∂F∂z

Q: The equation (5)/(3)log_(4)(x)=9 can be written in the form x=2^(y) for some number y. What is y ?

A: We have to find the value of y. Conversion of log form to exponental formlogbm=x                 →…

Q: If f(x) = x²= 1 and g(x) = 3x²=2x-1, + what is lim f(x) ? X→1 g(x)

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Q: Construct a related rates problem where the answer to said problem is 1.5 Please make the problem…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: How do I use the chain rule to find the derivative of (y=(cosx+2sinx)8)? I know (cosx=1) and…

A: Chain Rule of differentiation: If y= f(u) and u=g(x) , then y=f(g(x)) , so then                 dydx…

Q: Evaluate the integral. (Use C for the constant of integration.) [In(√x) dx

A: Short Explanation::-

Q: When a body is freed from a FIXED SUPPORT, what support reactions must be used to replace the effect…

A: This is question of support reaction  Here fixed support is given  And free body diagram related we…

Q: Evaluate the integral. (Use C for the constant of integration.) [7. 7z³e² dz

A: ∫7z3ezdz