Define the following hyperbolic function directly in terms of the exponential function (i) tanh(x)

Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d dr 11 t²dt =

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Q: (a) Find a unit vector u from the point P = point Q (17, 34). = NOTE: Enter your answer in the form…

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Q: Find the equation of the tangent line to the graph of the functic f(x) = 3x² - 4x +5 at the point…

A: Find out the equation of tangent line.

Q: Consider the function f(t) = 6 sec²(t) - 6t³. Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: The given function is: ft=6sec2t-6t3   As we know that; The expression for the antiderivative:…

Q: Use Part I of the Fundamental Theorem of Calculus to find each of the following when f(x) = [tªdt.…

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Q: S= [²3/1/20 The value of dr is

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Q: A particle is moving with acceleration a(t) = 6t+ 6. its position at time t = 0 is s(0) = 11 and its…

A: GIven: a(t)=6t+6 s(0)=11 v(0)=9   We know that, the integral of acceleration with respect to time…

Q: Given f(x) = x² + 4 and g(x)=√x-2. Find (fog) (x) and write the domain of (fog) (x) in interval…

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Q: • S X √x²-4 dx

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Q: Ronnie scored 8 baskets in his basketball game for a total of 18 points. How many two-point and…

A: Assume number of two points and number of three points and then go ahead.

Q: notation. Find the domain of the function -10c (3-1)(x+4)* O (-∞, -4) U (-4, 3) U (3, ∞) O (-∞, -3)…

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Q: For the following graph the equations and shade the area of the region between the curves. Determine…

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Q: 2 Given an = n² sin for all positive n converges Determine whether the sequence {an} Determine…

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Q: The value of of da T 1 -da is x² Submit Question

A: Given: ∫341x2dx

Q: What object is sliced to get conic sections? A pyramid A cone A sphere A cube

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Q: 3. Give an example of a situation in which composite differentiation might be used. Give examples of…

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Q: Provide the complete solution (typewritten if possible) for the item below. Consider the plane π…

A: The equation of the plane π is given as , x-2y+3z-1=0 and the line l is x=1-y2=z+1 Find the…

Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: Consider the function f(x) = (4-5x)7. Find the second derivative f" (1). O7(4 – 5z)® O-35 (4-5x)6…

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Q: Consider the function f(x) = 9 x³ Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) =

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Q: Suppose that h(x) = f(x) g(x) and that we know the following f'(3) = -1, g(3) = 2, & g'(3) = -5.…

A: Topic:- calculus

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: 8 №₁ 4-x² x+4.x² dx

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Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: Find the exact arclength of y = 2x3 for 0≤ x ≤ 2:

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Q: Find the average value fave of f(x) = x³ between -1 and 1, then find a number c in [-1,1] where f(c)…

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Q: 8 1 4-x² 4 x¹ +4.x² dx

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Q: tiderivative. Indicate which formula from the that you may have to do a substitution, or a tables!…

A: Ass per the guideline I am answering only one question at a time. ∫tan3x2dx

Q: O

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Q: Find the integral of f(x) = 1 √1-16x² between 0 and 1.

A: The given integral is 1/sqrt(1-16x2).

Q: Problem 7. (1 point) Find a solution to A(t) = dt 9A if A(0) = 3. help (fo

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Q: Factor x^2 + 10x + 12. (x + 5) (x + 7) (x + 10) (x - 12) None of the answers are correct; this…

A: Given: Factor x2+10x+12

Q: Evaluate: [² 3 x³dx -

A: Here we have to find the definite integral.

Q: Factor the following expression: x^2 +9x + 8 (x + 1) (x + 8) (x - 1) (x - 8) (x - 1)…

A: Solution

Q: 3. Algebraically rewrite the following equation using properties of logarithms and inverse…

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Q: Find the area of the region bounded by the graphs of f(x)=x^3-x^2+10x and g(x)=-x^2+26x

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Q: Consider the plane π : x − 2y + 3z − 1 = 0 and the line l : x = (1 − y)/2 = z + 1.      1.      Find…

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Q: 5. Prove the identity: cot(A + B) cot(A − B) = - cot² B tan² A tan² A cot² B - 1

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Q: Find f such that f'(x) = 9 √√x f(1) = 32.

A: Topic:- application of integration

Q: Question 17 > At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 21…

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Q: Approximate the area under the curve y = x from x= x³ with 6 subdivisions. = 2 to 5 using a Right…

A: The curve y=x3 from x=2 to x=5 we have to find the area under the curve using Right Endpoint…

Q: Evaluate the definite integrale dr.

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Q: 6) 3/2 · 4x²)³/; 9x dx

A: Our Aim is to solve the integral given below:-∫9-4x252x6dx -(i)

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

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Q: Question 19 Consider 7(a), the 3rd degree Taylor polynomial of f(a)= cos(z) centered at a IT Use the…

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: 1-y 2 Consider the plane π : x - 2y + 3z − 1 = 0 and the line 1: x= 1. Find the point of…

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: Use the graph of y = f(x) for problems 7 and 8. 1010 lim f(x) = 1; HI-4+ lim f(x) = 1; 41144 Use the…

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Q: 40 For problems 21 function to find t C 123, use the following. following rut o

A: We will find the required.