Find the equation of the line tangent to the graph of fat (1, 2), where fis given by f(x) = 4x³ - 9x² + 7. Use y as the dependent variable when you write your equation

Q: nd the missing value. y is directly proportional to x and inversely proportional to the square of z.…

A: Given query is to find the value of y.

Q: For the function h(x,y) : = əh ax ah ду || 7x+8y 5xy – 8 find əh ?х and

A: h(x,y)=7x+8y5xy-8∂ ∂x(xn)=nxn-1∂ ∂x(constant)=0

Q: The temperature at point (x,y,z) in space is given by T(x,y,z) = x + yz. A fly is at the point (1,…

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Q: Evaluate the integral. 5x 2x dx fate con in die 049 O ㅇ [sin 2x + cos2x) + C 12 sin 2x-5 cos 2x) + C…

A: We need to solve the following integral I = ∫e5xcos2xdx

Q: -Find the directional derivative of f(x, y, z) = x²yz+z³y, as you leave the point (1,1,1) heading in…

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Q: Find u and v if u+4v = 4i - k and 6u - v=i+j+k. NOTE: Enter the exact answers in terms of i, j and…

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Q: O False

A: For the graph of g(x) to be false ,we need at least  one point which do not satisfy.

Q: The profit (in dollars) from the sale of x lawn mowers is P(x) = 30x -0.03x² - 750. (A) Find the…

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Q: Macmillan Learning Find the interval of convergence of (x-4)" In (3n) n=2 (Use symbolic notation and…

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Q: An object's distance from a fixed point at t seconds can be represented by the function f(t) = 5t2…

A: Given function:- ft=5t2

Q: Question 11 The differential equation y' = 2y+sin x is Select the correct answer. O a. linear O b.…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: r Given z(x, y) = ln (2x + y²), a(r, t) = and y(r, t) = √r + t. t Find Əz Ət дz - Ət = Evaluate…

A: Givenz(x,y)=ln(2x+y2)x(r,t)=rty(r,t)=r+t   We are required to find:∂z∂t and ∂z∂tat r=10 and t=-1

Q: Find the length of the arc formed by 2 = 9y³ from point A to point B, where A = (0,0) and B = -…

A: Please see the below picture for detailed solution.

Q: Use the derivative of the function shown below to determine the open intervals in which the function…

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Q: In the figure below, set-up the integral expression when the area bound by the functions y = the x =…

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Q: Use the information given below to indicate whether the given scenarios express a function. (a) Let…

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

Q: dy Assume x and y are functions of t. Evaluate for the following. dt dy dt 3 y³ = 2x³ + 10; || dx dt…

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Q: 4. Practice similar Help me with this Calculate the integral, if it converges. If it diverges, enter…

A: The given integral is 1/(u2-4), limit from 0 to 2.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i - 4j as…

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Q: Find all the second-order partial derivatives of the following function. h(x,y)=2xe + 5y +9 2²h 2²h…

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Q: Question 6 Determine the center of mass (x, y, z) of the homogeneous composite solid with a…

A: Determine the center of mass?

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

A: To determine the convergence of the integral

Q: Evaluate the integral, if it exists. 5 19-x²|dx

A: G=∫059-x2dx

Q: Simplify. 2z 3x p + O [-2z+6x2 아 3æ-5 이 [2] 2z - 6x² 31-5 2z+ 6x² 31-5 2z+6x² -31 - 5

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Q: Differentiate the function using one or more of the differentiation rules. y: 1 = (3 + 2x5) 5 y' =

A: We know that, The SUM/Difference Rule: f±g'=f'±g' The Power Rule: ddxxn=nxn-1 The Chain Rule:…

Q: Question 4 For the integral: Write the integral again as: 0 0 x+2y+1 --LIT- V = -1 -(x+1) ? ? ? v =…

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Q: Find all the second-order partial derivatives of the following function. h(x,y) = 2xey + 6y + 8 22n…

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Q: II. Identify the equation of the slope of the tangent line, the slope, and th of the tangent line at…

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Q: Give the derivative formula for the function. f(x) = 2x−3 + ln(3)

A: Given : f(x) = 2x−3 + ln(3)

Q: Use the graph of the function f to determine its absolute minimum value and absolute maximum value,…

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

Q: Evaluate the integral. 3 ㅇㅇ 를 O 229 이름 sin³ 3x dx

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Q: Find the derivative of the given function. g(x) = x + ¹ g'(x) =

A: To find derivative

Q: The regular price of a pair of jeans is x dollars. Let f(x) = x - 12.50, where frepresents the price…

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Q: The equation of motion of a particle is s = t³ - 27t, where s is in meters and t is in seconds.…

A: Given motion particle:- s=t3-27t

Q: Continuity and differentiability are important conditions in many theorems in Calculus. One such…

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Q: Find the following limit. 25√√x - √√x 3³√√x +3¹/√x lim X→ ∞ 3 lim x→∞ 2³√x - √√x 5 3√x + 3√x 11 co…

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Q: Simplify. sin x csc x + sin x csc x O sin² x + 1 O 1 O csc x O2

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Q: By considering different paths of approach, show that the function below has no limit as (x,y)…

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Q: II. Identify the equation of the slope of the tangent line, the slope, and the equation of the…

A: To identify the slope of the tangent line, and to determine the  equation of the tangent line to the…

Q: 2 1) Fird dy using implicit differentiation X² + y ²³ = 7xy 2) Find the ein of the normal line to…

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Q: Consider the graph of y = f(x), shown below. 5 4 3 2 1 ਆਪਣੀ -3 -2 -1 1 2 3 14 5 -2 -3 -4 W The…

A: Given graph:-

Q: Verify the identity. cos x + cos x cot² x = cotx csc x Drag an expression into each box to correctly…

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Q: Angle x is a third quadrant angle such that cos x = What is the exact value of cos (2)? Enter your…

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Q: The function f(x) has tangent line equation y = 4(x-a)-6 at x = a. Both are shown in the graph…

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Q: Calculate all four second-order partial derivatives of f(x, y) fax (x, y) = -(4/y^2)sin(2x/y) fry…

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Q: By considering different paths of approach, show that the function below has no limit as (x,y) →…

A: Part A:

Q: Let u = (5,5), v = (1, 3), w = (17,-4). Find the vector x that satisfies 3u2v + x = 6x + w. NOTE:…

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Q: Zha begins 7 kilometers to the north of town, and rides his bike along a straight trail which leads…

A: Given Initial position, A (t=0) --> (10, 0)  Final position, B (t=4 sec) -->(0, 6)

Q: By the Horizontal Line Test, the graph below represents a one-to-one function.

A: Horizontal line test - If a horizontal line intersect the graph of a function more than once then…

Q: d² Find and simplify (f(x)g(x)) = O f'(x)g(x) + f'(x)g'(x) + f'(x)g"(x) + f(x)g"(x) O f'(x)g(x) +…

A: Given query is to find double derivative.