Utilize the definition of the derivative to prove that (sinx) = cos x

Q: This figure (la = 10.0 m/s²) represents the total acceleration of a particle moving clockwise in a…

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Q: 4. Solve the initial value problem explicitly for y(x): 2x+4y³√x² +12=0; y(0) = 2 dx

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Q: A factory with an assembly line can produce more automobiles per week as more employees are working…

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Q: - 1x² 2 xe de = 1 Proov this Note: Consider using by fart.

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Q: A rectangular aquarium having a length of 4 meters, a width of 2 meters, and a height of 3 meters is…

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Q: Find the arc length function for the curve y=18x*2 with starting point P.(1, 18). O z =…

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Q: In each part, complete the table and make a conjecture about the value of the limit indicated.…

A: Since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Find the derivative of y = x².

A: y = xx

Q: 2. (a) (b) Let f(x) = ln(x² − 3x + 1) d² f dx² df Find and dx Find an equation of the line tangent…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: X x +1 dx =

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Q: Consider the following function. g(x) = x³ + 3x²2 on [-3, 1] Find the derivative of the function. g…

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Q: 1. Suppose that f is a differentiable function and f'(x) ≤ 4 on interval [-5, 2]. If f(2)= 6, then…

A: Suppose that  is a differentiable function and on interval .If , then to determine the smallest…

Q: Suppose that the temperature T at point (x, y, z) is given by T(x, y, z) = sin(xyz) and that an…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: To find the x-intercept take x=0intercept:

Q: Use transformation to sketch the graph of the function g, then state the domain, range and…

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Q: Compute Ae, where ab sin(a) f dr A = 8 10 10 5 00 1 5 R -1 7 00 00 00 1.000 3 5 3 00 -5 10 9 3 52 a…

A: We solve the given problem using the concept of matrix multiplication.

Q: Find the area of the region under the curve y = f(x) over the indicated interval. 3 f(x) = sq units…

A: Given

Q: Graph the function. Then identify the​ domain, range, and​ y-intercept, and state whether the…

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Q: 3. Find by implicit differentiation for the curve e = x+y.

A: (3) exy=x+y

Q: Using Integration by Parts Evaluate ndx. +3

A: The given integral is

Q: 7. x - 4y = -10 -2x+8y= 20

A: Given

Q: given that h(x) = f(g(x)) where  f(x) = ln(x^2+1) and g(x) is a differentiable function with g(1)…

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Q: 3) a) Determine whether the sequence defined as follows is convergent or divergent: a₁ = 1 an+1 =…

A: We have to determine whether the sequence defined by…

Q: x

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Q: b NA (a) b AM (b) a

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Q: 7. For the iterated integral sketch the region of integration. [*[ f(x,y) dx dy

A: For the iterated integral to sketch the region of integration.

Q: A sample of a radioactive substance decayed to 95.5% of its original amount after a year. (Round…

A: Using radioactive decay law we can solve the question

Q: 0) at which the acceleration is equal to zero.

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Q: give that f(x) =3 sin x -2 cos x

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Q: Determine the number of equations and the number of variables in the following system of linear…

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Q: Evaluate [2x-3dx. x³ + x

A: I=∫2x−3x3+xdx

Q: Suppose that for a company manufacturing calculators, the cost and revenue equations (in dollars)…

A: The cost and revenue equations are given by,where the production output in one one week is x…

Q: 2. §13.3. Q8. Evaluate the indicated partial derivatives. (a). & (rev15ay). (b). (zers).

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Q: 1. A lead block has dimensions 8 mm by 6 mm by 2mm. To add value, the block will be covered in a…

A: We have to find the thickness of the silver coating.

Q: (b) Determine an equation of a polynomial in simplified form that has zeros of Find the member that…

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Q: Use the 3 step Mathematical Induction process to prove the following statements. You must label and…

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Q: The minute hand of a certain clock is 3 in long. Starting from the moment when the hand is pointing…

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Q: o expand the following expression as much as possible. Sin alculator. log₂ (2x² + 24x + 72)

A: The properties of logarithm to be used in the answer are: log(mn) = log(m) +log(n) log(m/n) = log(m)…

Q: 8. Halloween is fast approaching and we need to identify zombies. One sure-fire way is to give them…

A: In this question, we will find the double integral.

Q: Consider this graph of the function f to answer the questions below: -9 -8 -7 -6 -1 ↑f(x) 1+ -1 Ņ 2…

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Q: x³+sin(x) ex = _et f (x) Find f'(x) by using the quotient ule. Then use the product rule to find…

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Q: lim x-1 sin (x-1) x²-1 =

A: (2) L=limx→1sin⁡(x−1)x2−1

Q: For the following exercises, determine whether each of the following relations is a function. 1. y =…

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Q: Let A = -4 -2 9 -6 -10 -5 -10 -49 9 2 -3 5 -18 2 8 -5 0 7 0 9 -9 0 6 -7 -4 -1 2 -6 -3 -10 9 3 -7…

A: We have to find the entry at A41.

Q: Find d2y/dx2 by implicit differentiation. x 3y3 − 4 = 0

A: The objective of the question is to evaluate the 2nd  derivative of the given function.

Q: Solve the following exponential equation. Use logarithms to express the solution in its exact form.…

A: To solve the following exponential equation.

Q: Find the absolute maximum and absolute minimum values of f on the given interval f(x) = x-² In(x),…

A: f(x)=x−2ln⁡(x),[12,8]

Q: Write the function as a product of linear and irreducible quadratic factors, all with real…

A: Consider the function

Q: Suppose f is a differentiable function and its inverse function f-1 exists and is also differen-…

A: (5) f is a differentiable function and its inverse function f−1 exists