CНА x² +2x-35 Find lim x+7 X→-7 2. For f(x) = x³ + x² – Zx a. find the average rate of ch. b. find the instantaneous rate Differentiate the following

Q: Find partial derivative, zg and Zy for the following function: e 2x²+3y Z =

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Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: For n 4 we find the derivative of f(x) = x* as follows: f(x + h) - f(x) (x + h)* – x lim f'(x) = lim…

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Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: Suppose that z =x*y°,where bothx and y are changing with time. At a certain instant when x = 1 and y…

A: Derivative formula ddxxn= n xn-1Product ruleuv'=u'v+uv'

Q: 1 1. Given that y =- a. Find the average rate of change of y with respect to x over the interval…

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Q: B)ls w = z²1² analytical function or not?

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Q: Q4: Find the derivative of the function at Po in the direction of A 3) f(x, y, z) = xy+ yz + xz,…

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Q: 4. Differentiate the following function.   y=5e x−5x dy/dx=nothing   Enter your answer in the…

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: Please use Limits this is under calculus section

A: When x = 2, y = g(x) = 4 / (x - 1) = 4 / (2 - 1) = 4Hence, the point of tangency is (2, 4)

Q: 1 f(x) x – 2 Use the limit definition of the derivative to find (1) f' ( – 1) = (ii) f ' (0) = (iii)…

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Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

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Q: 2. Find the equation of the tangent to the functions g(x) = (x −4)² at its y-int. You must use an…

A: Solution:

Q: Let f(x) = 3x2 − 2x. (a) Find the instantaneous rate of change of f(x) at x = −1.

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Q: Find the derivative of the function h(s) = 5 + 7/8s by limit process

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: 17. For f(x) = x*, the instantaneous rate of change is known to be –32 at x = -2. Find the equation…

A: the given function is f(x) = x4 rate of change dydx=-32,          at x =-2

Q: Consider the function f(x) = x ² + 3. Part 1: Compute the slope of the the tangent line to y = x2 +…

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Q: Find the derivarlve find f2) uslv fla)= Linfatfay -a x-a Find derivative ECx)=3x"+| fiind f'(2)…

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Q: The impedance Z (ohms) in aseries circuit is related to the resistance R (ohms) and reactanceX…

A: Given that The impedance Z (ohms) in a series circuit is related to the resistance R (ohms) and…

Q: [8] Use the definition f(a +h) – f(a) f'(a) = lim h-0 h To find the derivative of the given function…

A: Given: So,          f'(2)=limh→0f(2+h)-f(2)h       =limh→ 012+h-12h       =limh→ 0-12h+2       Plug…

Q: Find (a) lim x--4- f(x), (b) lim f(x), and(c) lim f(x). X- -4+ x- -4 for x > -4 15) f(x) = ! x + 4…

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Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

Q: Find the derivative of the function by the limit process.

A: We have to find derivative of the given function by limit process: gt=t3+4t We know the derivative…

Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

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Q: Ax) = xin( ) given function calculate taylor poynomial of f(x) of degree 4 at a=4

A: Solve the following

Q: For f(x)=3x^4, find dy/dx using the definition, dy/dx=limΔx→0 Δy/Δx= limΔx→0 f(x+Δx)−f(x)/Δx.…

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Q: KL Let Y = (9x* +7L*) 4 (a) Find RK= YK'/YL, the marginal rate of substitution of L for K. YK RLK =-

A: Explanation of the solution is given below....

Q: dy Use the formula dx Ay lim f (x + Ax) – f(x) lim - Ax→0 Ax Ax dy when y = dx 1 to find x + 5 dy dx

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Q: Ax) = xin() given function calculate taylor poynomial of f(x) of degree 4 at a=4

A: solve the following, since previous question is not given so i can't evaluate error

Q: a) Find dx of the function y = (x+1)²using the limit definition of the derivative. b) What is the…

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Q: f(x) = x³, find using the definition, dx dy Ay = lim Ax-0 Ax f(x + Ax) – f(x) = lim Ax-0 dx Ax (a)…

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Q: Find dy by dx when  f(x) =2x²-x+5÷3x+2

A: The derivative of a function gives the rate of change of a function when an infinitesimal change is…

Q: f(x+h)- f(x) 4x3+9x+5 Using lim0 Find the slope of the tangent line y = Зx-8 h at x = -1.

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Q: Use f ′(x)=limh→0 f(x+h)−f(x)/h to find the derivative at x for the given function.   s(x)=8x+3 s…

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Q: (a) Find the derivative of y = f(x) =2x+1 using this definition f (x+h)-f(x) f'(x)= lim h (b) If x…

A: Differentiate above function with respect to x

Q: Explain the difference between the average rate of change of y as x changes from a to b, and the…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: dy at x = 2. dx 2 10. Given the curve y= 5 - (x-2)³, find (A) 3 -- (B) 3/2 (C) 5 (D) The limit does…

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Q: f(x) = 3-x/2x+

A: First we have to find derivative of function at x =-1 by using given forumla-

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

A: limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: 4. Determine lim 3x +x?. *--2 а. 10 с. 6. b. -2 d. -4 dy 5. Determine the derivative for y = 2x' -…

A: Dear student policy is to answer first one only yet I answering first three  for you kindly repost…

Q: Rank the functions x3, ln x, xx, and 2x in order of increasinggrowth rates as x→ ∞.

A: Given x3, ln x, xx, and 2x

Q: Q 1. a) Let y = x® – 5x³ + 5x* – 10. Then find minimum and maximum values. b). By using definition…

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Q: Consider the function y = g(x)= -x² + 3x +2. Compute g(2). Use the limit definition of the…

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Q: Q.NO.2: i. Find the limit Зх — sin(kx) lim - k + 0 ii. Find the relative extrema using both first…

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Q: 7. Use the limit definition of the derivative to find f'(x). Then find the equation of the tangent…

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Q: z = x2 + y2, where x and y are increasing at the constant rates of 2 units per second and 3 units…

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Q: H.W • Find f (x) of f(x)= by using the definition of the derivative. • 1- Find if y=3r-4 and t = Vx…

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