Find the following derivatives. z and Z₁, where z = 5x + 5y, x= 4st, and y = 5s + 6t Zs (Type an expression using s and t as the variables.)

Q: The demand equation for a certain product is given by p = 132 -0.09x, where p is the unit price (in…

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Q: The nature of the stationary point(s) of the function f = 13 x² − 12 y² +3 x +7 y O Maxima O Minima…

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Q: Find dy/dx by implicit differentiation. 4x² + 5xy - y² = 1 dy/dx =

A: Given equation, .Formula of derivatives:

Q: tan z f(x) = (sin x)

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Q: Consider the indefinite integral U x6 This can be transformed into a basic integral by letting (x7 -…

A: we need to find out the intergation.

Q: y=e³x - ex y X

A: Region bounded by y=e5x−ex,y=0,x=0

Q: 10. The equation 12x-05-3(y+6) represents the equation of the tangent line to the graph of g(x) when…

A: 12x−0.5=−3(y+6)

Q: Use implicit differentiation to find the slope of the tangent line to the curve at the specified…

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Q: 3) a) Determine whether the sequence defined as follows is convergent or divergent: a₁ = 1 an+1 =…

A: We have to determine whether the sequence defined by…

Q: X X+1 11

A: To evaluate the following integral.

Q: Figure 4.124 gives the derivative of g(x) on -2 ≤ x ≤ 2. a. Write a few sentences describing the…

A: Given graph of g'(x)

Q: 2-3 Given A = -3 -3 2, B= 0 1 -3 01 -2, find 2A 4B. 0-3]

A: A=[2−3−32−30],B=[10−3−20−3]

Q: (c) Does the volume of the cylinder of part (b) increase or decrease as t increases? (a) Find V'(t).…

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Q: 4. Solve the initial value problem below y"(x) = 4e²x8e-2x, y(0) = 1, y'(0) = 3

A: To solve the following initial value problem.

Q: 21. xy = 7; (1,7)

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Q: A student takes out a college loan of $4000 at an annual percentage rate of 4%, compounded monthly.…

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Q: Find dy/dx by implicit differentiation. x²y² + x sin(y) = 6

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Q: Recall that i = (1,0,0), j = (0, 1, 0), and k = (0, 0, 1). What are the vector and scalar compo-…

A: Given vectors are Let

Q: K Find the first and second derivatives. 6 X dy dx y = 5x-5 11 d²y dx² ||

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Q: Find the value D(3), where D is defined below. D(t)=3t−4

A: To find D(3) , substitute t = 3 in D(t)

Q: *+ 16xy + y^: 4x³ + 16y = 0 4y³ + 16x = 0 x³ y = / 7313

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Q: lim x-1 sin (x-1) x²-1 =

A: (2) L=limx→1sin⁡(x−1)x2−1

Q: Find dy / dx by implicit differentiation. 5x2 = 2 xy + 2x + dy / dx =

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Q: A price p (in dollars) and demand x (in items) for a product are related by 2x² - 5xp + 70p² =…

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Q: b. Find the derivative of the function. (x²+8) ³ y' = y =

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: State how many complex and how many real zeros the function has. f(x) = x² + 6x² - 4x² + 72x-192

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Q: Consider the function ƒ(x) = 7(x − 2)²/³. For this function there are two important intervals: (-∞,…

A: f(x)=7(x−2)2/3

Q: When writing the following linear system of equations in the matrix form A 421 + 3x2 = 5 -3x1-x2 =…

A: Given,

Q: 4. Solve the initial value problem below y"(x) = 4e²x - 8e-2x, y(0) = 1, y'(0) = 3

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Q: Solve the following differential equations: 2- ex+²ydy - e¹-2x dx = 0

A: given differential equation

Q: Let f be continuous on [-1,5], where f(-1) = 12 and f(5) = 6. Can we conclude that a value -1 < c <…

A: Intermediate value theorem states that if 'f' is a continuous function over a closed interval [a,b]…

Q: SHOW COMPLETE SOLUTION I. By integrable combinations, solve the following equations. (x³ + y)dx-(y²…

A: given differential equation

Q: The minute hand of a certain clock is 3 in long. Starting from the moment when the hand is pointing…

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Q: Perform a first derivative test on the function f(x) = 2x³ + 3x² - 72x+6; [-4,7]. a. Locate the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find an equation of the tangent line to the curve at the point (1, 1). y = x^e-x y =

A: to find the tangent line at (1,1/e) to the curve y=(x^4)(e^(-x))

Q: solve the differential equations 50 (1 + y²) dx + (2xy + y² + 1) dy =

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Q: Let f(t) = 6t2/3 + 5/3 (a) Find all partition numbers of f'(t). (Enter your answers as a…

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Q: Based on the graph of g"(x) pictured above, how many points of inflection exist for the twice…

A: As we know The inflection point exists when  and conavity changes  of function

Q: Let f(x)=√2+2x f'(5)= -2 X

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Q: Use the given graph of the function g to find the following limits (Note that if a limit does not…

A: Using the given graph we can find all the required limits

Q: Answer the following True or False. Sa 1 CSC x dx = ln(cscx) + C O True O False

A: The given problem is to identify whether the integral  trigonometric expression is true or false.

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 5xy - 4x² -…

A: We are given a function and we need to find out the relative maximum, minimum or saddle points if…

Q: Find the limit. sin(0) lim 0-00+ tan(0)

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Q: A particle moves with position function s = t4 - 4t³ - 20t² + 25t, t≥0 At what time does the…

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Q: Find a vector which is orthogonal to both v = (1,2,3) and u = (4,5,6). What is the area of the…

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Q: y' = y = eP(p + p√p)

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Q: Consider the function f(x) = 12x - 80x³ +6. f(x) has inflection points at (reading from left to…

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Q: Find the derivative of y = x².

A: y = xx

Q: unded by f(x) = √x, y = 0, and x = 4 is shown below. Find the volume of med by revolving the region…

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Q: Can we solve this without the Apply L'Hopital's rule.

A: Yes, we can solve this without using L'Hospital's rule.But we need some standard formula.