Find the Linearization L(x) of the function at a. b) f(x)=e^x+1 , a=0.

Q: 3. Write a formula that relates three different variables? (Hint: think about volume of geometric…

A: Solution : Given that

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Q: 1. Given [x² +1, 2x, x ≤ 1 x > 1. Is f differentiable at x = 1? Is it continuous at x = 1?. f(x) =

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Q: Find the general form of the quadratic function that has a vertex of (-4,-1) and a point on the…

A: Equation of quadratic function having vertex (-4,-1)

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Q: Find the transform of the given function by use of a table. f(t) = 5t sin (5t) + e-st cos (t) A…

A: Given : f(t) = 5t sin(5t) + e^(-5t) cos t

Q: 2x^2-4x+1/4x^2+1 determine the limit of n----> infinity an

A: Given query is to find the limit of the expression.

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A: Acceleration is given as the rate of change of velocity with respect to time.

Q: Hi can you type out the answer cause the answer is kinda messy

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Q: Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(8x)

A: Please see the below picture for detailed solution.

Q: Find the values of x, y and z that correspond to the critical point of the function ƒ(x, y) = 2x² +…

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Q: (a) In each of the following problems, you may assume that an exponential growth and decay model…

A: Solution: 2(a) (i) N0=200 g , N(t)=140 g, t=10 years

Q: Find the solution of the given initial value problem: y (4) + 2y" + y = 9t + 10; y(0) = y'(0) = 0,…

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Q: is the triangular region with vertices (0, 0), (3, 0), (0, 2)

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Q: f(x) = cos 2x - 2 cos x on [0, 2π]

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Q: A function h is dependent on x and is differentiable for all real numbers. Let f be the inverse of…

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Q: INTEGRAL CALCULUS (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG…

A: We will find the required.

Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

A: Topic -Partial fraction decomposition We are given, 3x(x-1)2(x2+3)

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Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

A: need to find out the critical point.

Q: Calculate the integral of f(x, y) = 4x over the region D bounded above by y = x(2 - x) and below by…

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Q: 1. An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting out x-inch by…

A: Topic -Application of derivatives We are given a cardboard of 20 inch by 32 inch and we need to find…

Q: The radius of a increasing at a At what rate is the circles. circle is rate of -2 m/s. circumference…

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Q: 2. Determine f'(x). (a) f(x) = √26

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Q: CSC 3/¹² (3x) cot³(3x)d

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Q: Use the degree 2 MacLaurin polynomial of f(x) = cos(2x) to approximate cos(2). . (Enter a number for…

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Q: f(x)=10x

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Q: A set equation is not an identity if there are examples for the variables denoting the sets that…

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Q: 3) Suppose that f mx² + ax + bdx = m, a, & b are constants and C is an arbitrary constant. For each…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. sin(In 41x) X dx

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Q: 2. Separation of Variables Determine which of the following differential equations are separable. Do…

A: 1) y'=1+ydydx=1+ydy1+y=dx Therefore given differentiable function is variable separable.

Q: A strain of Staphylococcus aureus doubles every 8 hours. A colony of 20000 was cultured in a petri…

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Q: Find the absolute extrema of f on the indicated interval. f(x) = −3x¹/³(x − 32) on [-1,27]

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Q: Find the general form of the quadratic function with the vertex (2, 1) and a point on the graph (-2,…

A: The quadratic function has vertex at 2,1 and a point on the graph -2, 17. We have to find the…

Q: √x² ²-4 .3 x -dx

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Q: Find the linear approximation at x = 0 to show that the following commonly used approximations are…

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Q: a) Determine the parent function and sketch its graph. -10 -8 -6 b) Find the x-intercept of f(x). c)…

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Q: Find the inverse transform of the given function of s. F (s) = 6s - 49 s2-8s +41 A) f (B) f C) f =…

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Q: 2 3...... 2 y...) + Xdy =0 where yo...

A: Given differential equation  (2xy−1)dx+x2dy=0

Q: Find the f(t) = 1- cos 7t transform of the given function by 7 A F (S) - 2+49

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Q: What is t' (x) if t(x) = Select the correct answer below: = 80x5 .? ex O t'(x) O t'(x) = 80( -). ○…

A: Given query is to find the derivative of the function.

Q: The second derivative of the function g is given by g" (x) = 0.15 0.29x4-0.694x³ + 1.9136x2. At…

A: To check the inflection point,    It is enough to check whether g"(x) =0 or not.

Q: 2x - 4 Find f ' (x) using the definition of the derivative: f ' (x) = lim h>0 f(x+h)-f(x) / h

A: Given query is to find the derivative using definition.

Q: A particular type of bacteria is found capable of doubling in number 49.4 minutes. every N of…

A: Topic- Exponential function We are given,the number N of bactria present after t minutes…

Q: Evaluate the following integral. 2x + 5 2 x + 25 X 2x + 5 2 x + 25 dx dx =

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Q: Question Let h(x) = f(x)g(x). If ƒ(−6) = 4, ƒ' (−6) = −2, g(−6) = 2, and g'(-6) = 5, what is h'(-6)?…

A: Use product rule of differentiation.

Q: A boat is towed toward a dock by a cable attached to a winch that stands 6 feet above the sea level.…

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Q: Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle…

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Q: Find the linearization. L(x) of f(x)=x² +1/x a+x= 1₁

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