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Q: Find an equation of the tangent line to the graph of the function at the given point. y = (e4x − 4)...

A: We first have to find y'We apply exponent rule and chain rule.y'= 8(e^(4x))*(e^(4x)) -4)

Q: Can you help me step by step with this problem?

A: Firstly, we set u=2t and v=(3t^2-70)^5, then we fid du/dt and dv/dt

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A: Given,

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A: To find the limit of the function f(x) at x = 8, where the function f(x) is given below:

Q: Calculus Question

A: To study the motion using derivatives

Q: We say a function f is even if f(x)= f(-x) for all x in its domain. We say f is odd if f(-x)= -f(x) ...

A: Given,

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A: Given,

Q: Derive the 1st Shifting Property from the defifinition of the Laplace transform.

A: First shifting property:If,

Q: Evaluate the limit. (Use symbolic notation and fractions where needed.) 35x27x1/3 lim = V25x4 +5

A: Consider the given expression:

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A: Given,

Q: Can you help me step by step with this problem?

A: Obtain the derivative of the given function as follows.

Q: A lump sum of $1000 is invested at 4.5% compounded continuously. (a) Write the function for the mode...

A: From the given information, the initial amount is $1000 and interest rate is 4.5% or 0.045.(a)Obtain...

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A: Observe the first graph.

Q: For function z = f(x,y) where f(x,y) = 4−x2-2y2 , we compute that fx(1,1) =−2 and fy(1,1) = −4. We h...

A: The problem concerns vector and scalar equations of lines and planes associated to the given surface

Q: 83

A: Given, 

Q: i need help with questions 25-37 please and thank you

A: Consider the given function.

Q: Find the derivative of the function. State which differentiation rule(s) you used to find the deriva...

A: First write the expression with exponent (for the rational part)

Q: Find the inverse of f(x)=3x−5/5x−2   f−1(x)=

A: The way you have written f(x), it has many intepretation. I am using the interpretation of f(x) as s...

Q: solve-  (sin π/4 cos π/6− sin π/6 cos π/4) ^2

A: Given, 

Q: Let f (x) = e9x.Find a formula for the n-th derivative of f, for n ≥ 1.You may use e (the natural nu...

A: Given function is:The first derivative of the function is given by:Using the chain rule: The second ...

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 15 and f'(2) = 4 (Use symbolic notati...

A: To write down the equation of the tangent using the given data

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A: Given,Side of cube = 7 inches

Q: Show a complete solution ry-sy13, ty

A: Given:Differential equation:

Q: I need help on my Calculus HW. I am suppose to find the limit for question #49 in Section 3.3 (page ...

A: Consider the given limit function.

Q: FInd the derivative.

A: Find derivative of

Q: Consider the piecewise-defined function f defined by 8 -3x2 11 6x { if x 1 if x 1 f(x) Find f'(1). I...

A: Given,

Q: (a) Draw a line tangent to the graph at point P. hundred hundred thousand thousand 60 50+ 50 40 40 y...

A: Estimate the slope of the tangent line.

Q: Can you help me with this problem step by step?

A: Consider the given function.

Q: find the limit

A: The given limit to be evaluated is,

Q: How to do intermediate value thereom f(x)=2x3+6x2-8x+2 : [-5,-4]

A: Consider the given function

Q: An airplane is flying at an elevation of 5150 ft, directly above a straight highway. Two motorists a...

A: To determine the distance between the two motorists.

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per second...

A:

Q: How do you solve an inequality with an absolute value and with a fraction?  I am dealing with the ab...

A: To discuss inequalities involving absolute values and fractions

Q: Can you help me with this problem step by step?

A: The given equation is x = cot y.Differentiate both sides with respect to x.

Q: sec 0 1 23. lim ө 00

A: The given limit is

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A: GIven, 

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A: Consider the given function

Q: i am having trouble with part c i have one more chance to get it correct

A: Part (c)To find the average rate of change of profit when the ticket price rises from $350 to $400.

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A: The given Figure can be redrawn as follows.

Q: Can you help me step by step with this problem?

A: Obtain the first derivative of the given function as follows.

Q: Can you help me step by step with this problem?

A:

Q: A board 20 feet long slides down a wall. At the instant the bottom end is 16 feet from the wall, the...

A: Given: Length of ladder is 20 ft. sliding down a wall. Distance of the bottom end from the wall is 1...

Q: Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is a...

A: Given function, 

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A: Sum of three angles of a triangle=180 Two of them are 90 and 48.B=180-(90+48)= 42Answer: B=42 degree

Q: When a rocket is 3 kilometers high, it is moving vertically upward at a speed of 400 kilometers per ...

A: Let the height of the rocket be h and the angle of elevation from the observer’s eye is x.

Q: I don't know understand one and it's parts.

A: Given,

Q: The curve with equation  y2 = 5x4 − x2  is called a kampyle of Eudoxus. Find an equation of the tang...

A: Given:

Q: (x2+ 1)(x tan 8 dx 81. dx 3) (x+2)3 dx (sin (sin (e*))) 83. (In (sec x tan x)) dr dx xex P (sin (e+1...

A: We’ll answer the first question since the exact one wasn’t specified.Please submit a new question sp...

Q: f(t) = tan(sec(cos(t)) take the derivative of this function

A: The given function is,

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A: Consider the angle C is 90 degree and the angle A is 42 degree.The angle B is computed by the formul...