Find an equation of the line that is tangent to f(x) = x and parallel to the line y = 3x + 1 (Hint: Sketch the graph. Parallel lines have the same slopes) *Use GeoGebra or Desmos graphing calculator for easier sketching of graphs.

Q: Find the volume formed by rotating about the y-axis the region enclosed by: x = 2y and y = x with y ...

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Q: Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an ar + (- ...

A: Given: - The sequence is, 7+5+3+......+(-263)=∑k=1119(3k+1)= To compute: - The sums below. (Assume t...

Q: 2.(Easy) In each of the following, verify that the given expression is either an explicit or implici...

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Q: f (t) = t5 e(1-t)

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Q: Find the surface area of revolution about the x-axis of y=7x+1 over the interval 1 ≤ x ≤ 3

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Q: Identify the most appropriate differentiation rules to be used in finding the derivative of the foll...

A: Given :1) y=(2x+7)-(x2+3x-1)find tangent :2)f(x)=1x at x=23) f(x)=x-2x+3 at x=2

Q: A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s ...

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Q: 5) Find the scalar and vector projections of b onto a. a = 5i – k, b= i + 2j + 3k %3D -

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Q: Write the following as the sum and/or difference of logarithms. Assume all variables are positive. T...

A: Given,logx12y17z6By using properties of logarithm:1. log(am)= m log(a)2. log(ab) = log(a) - log(b)3....

Q: 1, 2, 3> and B = , P = (9, 8, 7) s the angle between A and B? (I should not have to specify this, bu...

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Q: Find the local linear approximation L(x, y) to f(x, y) = x^3y^5 at P(2, 1) and simplify. (b) Find th...

A: Here, the given function is: f(x,y)=x3y5 and the given point is P(2,1).

Q: Find the indicated derivative and simplify. y' for y = (2 + 7x- 9x²) ex y' =]

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Q: In Exercises 19–22, find the slope of the curve at the point indicated. x - 1 y = x + 1' 22. x = 0

A: Find the slope of the curve at x= 0 is  y= (x-1)/(x+1) 

Q: 75 ft A pole stands 75 feet tall. An angle 0 is formed when wires of various lengths of a feet are a...

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Q: Solve the IVP: y" + y' = 0 y(n) = 0, y'(1) = 2, y'"(n) = -1

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Q: the error estimate for Taylor polyno

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Q: Droids on the planet Tatooine perform calculations in base-6. What is the largest base-6 number that...

A: The digits in base 6 are (0-5) (0,1,2,3,4,5).  

Q: The figure below shows a function g(x) and its tangent line at the point B=(1.6,8.6). If the point A...

A: NOTE: Refresh your page if you can't see any equations. . the function has a tangent line at point B...

Q: 1. Differentiate by using product rule. You do not need to simplify. 9. y = (5x* – 8x +)(2x6 – 5) x3

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Q: If f(x) = (3, -1) what are the coordinates of f(x) = -r(-3x) +1? (4)

A: Find your answer below 

Q: Given: cosA= -4, sin x = - ,e is in the third quadrant, and x is in the fourth quadrant; evaluate co...

A: Given:- cosθ= - 4/5 , sin x = - 12/13, θ is in the third quadrant, and x is in the fourth quadrant; ...

Q: Find the point on the line 5?+2?−2=0 which is closest to the point (0,0).

A: Find the point on the line 5x+2y−2=0 which is closest to the point (0,0). here we can first find the...

Q: Calculate the derivative. y= cos x In (cos ?x) y' =D (Use parentheses to clearly denote the argument...

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

Q: Solve using variation of parameters: y" + 5y' + 4y = 2e¬* 1. Find yc 2. Find u1 & u2 3. Find yp

A: See the details solution in below

Q: 6.(Straightforward) Solve the separable ODES: (a) dy/dx = sin 2x. (b) dx + e* dy = 0. (c) xdy/dx = y...

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Q: A graph of y= f(1) is shown. In the same coordinate system, sketch a graph of the derivative functio...

A: The given graph is of a parabola with the vertex (0,-1). So, its equation is: y=a(x-0)2-1⇒y=ax2-1......

Q: Determine whether the series is convergent or divergent. n- 1 5n – 1 n = 1 convergent O divergent If...

A: The given series is  ∑n=1∞ n-15n-1

Q: The voltage V across a resistor in an electric circuit is the product of the resistance and the curr...

A: We have to find dv/dt at t=5 seconds.

Q: Differentiate the following function. 8. L(t) = Vt L'(t) =

A: Explained below 

Q: Derivative Calculations In Exercises 1-12, find the first and second derivatives. 4. w = 3z7 – 7z3 +...

A: Derivatives first and second   

Q: Let f(x) = x- 2x- 9. a. Find the values of x for which the slope of the curve y = f(x) is 0. b. Find...

A: Topic:- derivatives

Q: 16. What is the derivative of f (x) = e8x+3? %3D a. f'(x) = e8 b. f'(x) = 3e8x c. f'(x) = 8e d. f'(x...

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Q: The graphs of x = 5, y = f(x) (solid) and y = g(x) (dashed) are shown; the graph is not drawn to sca...

A: We have to create the integral form of above graph. 

Q: In Exercises 9–18, write the function in the form y = f(u) and u = g(x). Then find dy/dx as a functi...

A: Note: as per guidelines I have to solve only 1 question so please repost question 38 in next window....

Q: Consider the following shaded region bounded by the curves y = x/2 and r = y² – y - 4. (a) Draw a re...

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) %D (1 + x)5 00 f(x) = ...

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Q: A person is holding a kite 5 ft above the ground. The kite gets stuck on a 20 ft tree. As the person...

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Q: lim sin (x + x - 22

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Q: The voltage V across a resistor in an electric circuit is the product of the resistance and the curr...

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Q: If f(x) = 6*2X, then f"(x) = %3D %3D Select one: a. 6*2% (In (2))2 O b. 36 *2% (In (2))2 O c. 6* 4x ...

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Q: Please show every step I want to understand why my answer

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Q: 4. Te- 105 has a half life of 203.9 hours. If there are 1054 g of Te - 105 initially, how long will ...

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Q: me

A: We will solve the integration using substitution. 

Q: In Exercises 7–12, find the indicated derivatives. dr 8. if r= s - 252 + 3 ds

A: Topic:- derivatives

Q: 2. Jenna is borowing $800 from her parents to buy a mountain bike. plans to pay them back at the rat...

A: Given: - Jenna is borrowing $800 from her parents to buy a mountain bike. She plans to pay them back...

Q: Find the nth Taylor polynomial for the function, centered at c. f(x) : 1 n = 4, c = 5 Pa(x) = %3D

A: A Taylor series is given by          f(x) = ∑k=0∞ fk(c)k!x-ck = f(c) + f'(c)1!(x-c) + f''(c)2!(x-c)2...

Q: 2. Find the domain of the following functions: 3 a). h(2) = %3D 4-2 b). f(x) = VE– 4 c). g(u) = 4.

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Q: 3) y =-1+ 3cos 0 T元 3元 2元 5元 3元 一2 不一2

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Q: Find the area of the surface generated by revolving the curve - 5x y = e-b", x > 0 around the -axis.

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Q: 2. Consider the shaded region to the left of the y-axis bounded by the curves y = x2 – 1 and y = x2/...

A: 2) Here, the region is bounded above by the curve y=x22 and below by y=x2-1.