Determine the derivatives, dy da dy da (1) y=e¹ ⇒ (2) y=x4 ⇒ dy da Y of the four given curves.

Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = xy + yz + zx, Po(1,-1,2),…

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Q: Let f(x)=3x+2x^3 Find f^-1(22)

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Q: Differentiate the following function: u' u= √√/t² +2√//t³

A: As we know that, The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And a·f'=a·f'  ,…

Q: 10. f(x)=x²+6x+5 a. Find the vertex using the vertex formula. b. Find the intercept(s). c. State…

A: Given equation:- fx=x2+6x+5

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

A: A detailed solution is given below.

Q: 10) Two planes leave an airport at the same time. Their speeds are 130 miles per hour and 150 miles…

A: Given: Two planes leave an airport at the same time. Their speeds are 130 mph and 150 mph, and the…

Q: How would I draw the following ellipsoids? 9x^2 + y^2 + z^2 = 9 9x^2 + 4y^2 + 36z^2 = 36

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Q: find the absolute maximum and absolute minimum of the function x - 2cosx  on the interval of (-2, 0)

A: we can find the absolute maximum and minimum .

Q: y' = Differentiate y sin z 28

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Q: Determine whether the series converges; if so, find its sum. If the series diverges, indicate that…

A: Given series is ∑k=1∞54k-45k

Q: Given x + y +z = 4 and Po(2,2,0), find the following. (a) Find the equation for the tangent plane at…

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Q: Consider the following function. s(t) 11.8 1 + 3.8e3.6t (a) Identify the logistic function as…

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Q: How do you find the absolute minimum, absolute maximum, and critical point?

A: This is a problem related to Maxima and minima of the function. Please follow the procedure given…

Q: ation to find the derivative curve at the given point. dy dx

A: given curve is :-y2= 5x point (45,15)then by using implict differentiation , we have to find slope…

Q: 1. For what value(s) of his -4 3 h 5 {[H²H]} -7 € Span

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Q: How would I find the limit of the following quotient? sin(x^2 + y^2) / (x^2 + y^2) lim…

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Q: 54. lim x→0 sin 3x sin 5x x²

A: Please see the below picture for detailed solution.

Q: a) Sketch the function y + yx² = x

A: The answer is in step 2.

Q: A water balloon is thrown upward from a window that is 75 meters high with an initial velocity of 19…

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Q: Identify the location and value of any relative maxima or minima of the function. Part: 0 / 2 Part 1…

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Q: Suppose the derivative of a function f(x) is df/dx = (x-8)(x+4)(x-3). Are the below values local…

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Q: GIven f(x) = 2x^2, x = 2, h = 0.1. How would I approximate the derivative three ways using the…

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Q: S 1 √4x²+81 dz +C

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Q: Suppose that the surface area, S, and radius, r, of a sphere are changing with respect to time and…

A: Given query is to find rate of change at indicated points.

Q: (b) Find all the values of such that matrix B is a singular matrix. 1 λ λ2 B = 1 1 1 1 3 1 9

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Q: Find the derivative of the function f by using the rules of differentiation. f(x) = (1 + 2x²)² + 3x³

A: We need to find the derivative of  fx=1+2x22+3x3

Q: Find the equation for which y" = 6x² and which passes through the point (0,2) and (-1,3).

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Q: Write an equation for a rational function with: Vertical asymptotes of x = 6 and x = 7 x intercepts…

A: Given query is to find the function.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Find T, N and B for the curve r(t) = (4 cos(5t), 4 sin(5t), 2t) at the point t = 0 Give your answers…

A: To find T→, N→, and B→ for the curve r→t=4 cos5t, 4 sin5t, 2t at the point t=0.

Q: 10) A lifeguard is watching a beach from a line of sight 6 feet above the water. She sees a swimmer…

A: ( 10 ) Given height above the water = 6 ft depression =8°

Q: Assuming annual​ compounding, find how long it would take for the general level of prices to double…

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Q: Suppose a company has fixed costs of $300 and variable cost per unit of 2x +1460 dollars, where x is…

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Q: Find the absolute maximum and absolute minimum of the function z = f(x, y) = x² - 10xy +10y on the…

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Q: Find the exact length of the curve. x = 5 cos(t) = cos(5t), y = 5 sin(t) = sin(5t), - 0 ≤t≤1

A: Given: x=5cos(t)-cos(5t)y=5sin(t)-sin(5t)0≤t≤π To find: The length of the curve

Q: 66. In the diagram below, AB and CD are two parallel chords of circle O. If AB=6, CD=12, and the…

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Q: Find the average value of f on [0, 16]. fave 11 YA 1 0 4 8 12 AX

A: see below the answer and calculation

Q: Let f(x) = 8x + 6-15e. Then the equation of the tangent line to the graph of f(x) at the point (0,…

A: Given query is to find the equation of the tangent.

Q: Find all zeros (if any) of the quadratic function y = 2x² - 2x - 7. NOTE: Enter your zeros exactly.…

A: Given query is to find the zeros of the quadratic.

Q: 21. Suppose the last column of AB is entirely zero but B itself has no column of zeros. What can you…

A: This is a problem related to matrix operations. Please follow the procedure given below.

Q: Find the x- and y-intercepts. -5x-8y = 40 Write each intercept as an ordered pair. If there is more…

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Q: over Z5 Perform the following calculations (a) 2.3 = = (b) 3.4-4 (c) 4-1 =

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Q: For the equation given, evaluate dv 5exy - 4x = y 7 dy at the point (3, 0). (Round your answer to…

A: Given query is to find derivative at indicated point.

Q: 2.1, #17: For the graph of g given, arrange the following numbers in increasing order and explain…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: Find all exact solutions to the following trigonometric equation for on the interval [0, 2π]. Show…

A: To solve the given trigonometric equation

Q: Find the negative and positive tangents of 2x3+6x2+90x+4

A: Let given function = f( x ) f( x ) = 2x3+6x2+90x+4

Q: Find the value of b and e of the piecewise function f(x) = (bx² + 3 lc - 2x ,x≤2 , x>2 Where; lim…

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Q: Solve the following DE. ( Variable Separable )  x2(y+1) dx+y2(x-1)dy=0

A: Here we have to solve the differential equation.

Q: Identify the location and value of any relative maxima or minima of the function. If there is more…

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Q: Determine the center and radius of the circle. (x+6)² + (y− 5)² = 64 Part 1 of 2 The center is (…

A: As we know that, The standard form of equation of the circle is: x-h2+y-k2=r2 Where: The center is…