Differentiate the functions: a. k(t) = et + te b. y = e-3xsin3x c. y = (ex) / (1 - ex)

Q: I) Consider the function: y = + C,e2x + C,e-5x + Czxe-5x

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Q: dP dt т 1- kP 1- M

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Q: Find an analytic function whose real part is u(x, y) = x³y - y³x 7²+1

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

Q: Determine an approximate solution of the equation z3 + 3xyz? – 5x²y²z+ 14 = 0 for z near 2, as a…

A: To determine : an approximate solution of the equation               z3+3xyz2-5x2y2z+14=0 for z near…

Q: An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed…

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Q: The function f(x, y) = -3y + 2√√ry is a

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Q: Find the linear approximation of the function f(x) = Vx+3 at a = 1 and use it to approximate the…

A: Given the function fx=x+3. Find the linear approximation of f(x) at a=1 and use it to approximate…

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Under certain conditions, the wind speed S, in miles per hour, of a tornado at a distance d feet…

A: Given wind speedSa,d,v=av0.51 d2

Q: Differentiate the function.  u= (1/t -1/square root of t)^2

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Q: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: Differentiate the function. 2. y = (4x – 5)* (4 – x³) ² dy 13|

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Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: Differentiate the function. y = (3x- 2)² (1 –x³)² dy

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Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

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Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

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Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

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Q: the temperature of a pot of coffee after brewing can be determined by the function…

A: Given temperature function is: F(t)=104e-0.0245t+76

Q: for f(x)=2x4-5x3+7 find all potential points of inflection and map the intervals where the function…

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Q: As machines get older, the cost of maintaining them tends to increase. Suppose for a particular…

A: Answer to the subparts are given ,

Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

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Q: The cube root parent function y = Vx has been transformed a) 2.

A: given graph

Q: A​ once-popular children's doll is slowly declining in popularity. The quartic function…

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Q: For the function y = f(x) = x² – 2x, x x ≥ 1, find (ƒ-¹) '(3) = df-1 dy y=3

A: We have to find the f-1'(3).

Q: The Cobb-Douglas production function for an automobile manufacturer is f(x, y) = 100x0.6,0.4, where…

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Q: Find the linearization for f(r) 10, and use it to approximate 12 near a=

A: We want to find the approximate value of 112 by linear approximation of the function ,fx=1x by…

Q: y = V4x3 –6

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Q: Find f(4) using forward, backward and central difference of: (3 – 2x)2 f(x) = %3D x2 Step size = 02

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Q: Evaluate the function: S 4ry(6+y/2)dy

A: topic - indefinite integral

Q: The derivative of the function y = 7x² + 12 – is: - 15 a) y' = 14x + x2 15 %3D b) y' = 14x + %3D c)…

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Q: Differentiate the function.  v = t2 - 1 / fourt root of t3

A: Given function is v=t2-1t34. Power rule of differentiation states that: ddxxn=nxn-1 Differentiating…

Q: Find the analytic function whose imaginary part is v =2xy

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Q: The function f(x, y) : 1+2? +y? is 1-x2 -y? discontinuous at the points {(x, y)\æ² + y² # 1}. True…

A: The given function is f(x,y)=1+x2+y21-x2-y2

Q: For the function f(x,y.z) = 3 + 4xy - 5z*, find f,, f, and f,.

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Q: A once-popular children's doll is slowly declining in popularity. The quartic function f(x) = -…

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Q: For the function f(x,y) = 5x² + 6y², find f(x + h,y)-f(x,y) h 11 f(x + h,y)-f(x,y) h

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Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: Find the inflection point(s) of the function f(x) = 2eX. %3D (x, y) (smaller x-value) %3D (x, y) =…

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Q: of the function. + 3y + 11

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Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: 2.Find all the maxima value of f(x, y) = 49 - x2 – y?, on the line x + 3y = 10 %3D ||

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Q: 1. Plot the function f(t) = (x+5) %3D 4+3x2 for -35 x 5.

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Q: The derivative of the function f(a) a-8x +9 at the number a is %3D 2a – 8. - TRUE O FALSE

A: 1.Given,            f(x)=x2-8x+9

Q: Differentiate the function. y = In(12 + t – t³1) y' =

A: Here we differentiate the y with respect to t

Q: Differentiate the function P = 5t³ + 4e'. dP dt

A: GIVEN: P = 5t3 + 4et TO FIND: dPdt

Q: Determine the extrema of the implicit functions: (2² + y² + z²)² = 1 – a² – 2², z = 2(x, y) | |

A: Given x2+y2+z22=1-x2-z2 Differentiate with respect to x:…

Q: (b) Find the Linearization of the function: f(x)= Vx at a= 27 and use it to approximate the number…

A: Let the function is f(x)=x3 Let a = 27   Formula: Linearization of the function f(x) at x = a…

Q: Find the line tangent to the function at the indicated point: f(x) = v8x² – 4x ;x = 1 ОУ-12х-10 o…

A: Since there are multiple questions present and you have not specified which question to answer,…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.