Suppose that 8 J of work is needed to stretch a spring from its natural length of 40 cm to a length 60 cm. How much work is needed to stretch the spring from 50cm to 70 cm? Give the exact answer in the simplest form and Show All Your Work.

Q: 3. You may use your graphing calculator for this problem. Make sure to explain your answers, includi...

A:

Q: 는 (-10x4). Find dx Provide your answer below: d (-10x-4) = [D dx

A:

Q: ow directly that the given functions are linearly dependent on the real line. That is, find a nontri...

A: Topic:- algebra

Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show tha...

A:

Q: In(x) Find the maximum and minimum values of the function f(x) = on the interval [1,6] by comparing ...

A:

Q: Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations.) x...

A: When the degree of numerator is greater than degree of denominator then there is no horizontal asymp...

Q: Express the sum using summation notation. Use the lower limit of summation given and k for the index...

A: We have to calculate summation

Q: 2х + 6, х 6 From the following results, determine whether the function f(x) = is continuous at x = ...

A:

Q: Find the derivative of f(x) = -4x ( 3' *(3"). %D 3+4

A:

Q: Given y = f(u) and u = g(x), find dy dy dy du by using Leibniz's notation for the chain rule: dx dx ...

A: Given y=fu and u=gx, to find dydx by using Leibniz's notation for the chain rule: dydx=dydududx.y=5u...

Q: Find a value a > 0 so that the graph of the exponential function f(x) = a" contains the point (3, 1/...

A: The point lies on the curve, so the point satisfies the given function.  

Q: Find tan x dx.

A:

Q: Find

A:

Q: 39. Using Properties of Definite Integrals Given L fe) dx = 10 and fe) dx = 3 evaluate (a) dx. (b) d...

A: Given query is to find the value of indicated integrals.

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r ...

A:

Q: Find the area of the surface obtained by rotating the curve y = V1+ e, 0sx<1 about the X-axis. 2). S...

A:

Q: 7t + 4 lim t→-∞ t2 + 1 – 7t

A:

Q: 2. Solve the following differential equations. (a) y' = x2 – xy+ 1. (Hint: Consider the subsitution ...

A: Both the parts have been solved in detail. 

Q: The function f(x) = 6x¬1 for the interval (1,3) has a local minimum. a local maximum. both local min...

A: Note :- As you write for solution only for interval [1,2] so i  am providing solution only for it.

Q: 4. A concert promoter has found that if she sells tickets for S50 each, she can sall 1200 tickets, a...

A: Explanation of the answer is as follows

Q: 1. f(x) = x² and g(x) = –x² + 12x – 18 have a common tangent at point P. Determine the equation of t...

A: for same tangent line  slope of equation is same f'(x) = 2x g'(x) = -2x +12 both are same so f'(x) =...

Q: 1.)C

A: Please refer to the image below

Q: 6. Given that k is an arbitrary constant, find the orthogonal trajectories of the following family o...

A:

Q: (a) Show that the following identity is true 1 1 2n +1 n2 (n+ 1)² n²(n + 1)² (b) Use the identity in...

A: Sum

Q: (3x²-5)°(4x³-7) 4. Find the derivative of f(x) DO NOT SIMPLIFY (first step only) (2x-1)*

A:

Q: Find the derivative of y Cos3 3x+8 (x). %3D Provide your answer below: y = D

A:

Q: Write the expression as a single logarithm with a coefficient of 1. (a) In(13) – 2 In(4) + In(32) (b...

A:

Q: /+v= y, y(0) = 2

A:

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

A:

Q: 3. Find the relative maximum and minimum values and saddle point(s) of the function, S(x, y) = 2a + ...

A:

Q: Sketch the graph the integrands and use areas to evaluate the integrals. La |(1- l2) dx а. -1 3/2 (-...

A:

Q: Enclosing the Largest Area The owner of the Rancho Los Feliz has 2940 yd of fencing to enclose a rec...

A:

Q: 5x + 400 A garden shop determines the demand function q = D(x)%= during early summer for tomato plan...

A:

Q: dx 4x

A: Given query is to find the value of the integral.

Q: The regions A, B, C, and D in the figure below are bounded by the graph of the function f and the x-...

A: Given query is to find the average value of the function.

Q: Find an algebraic expression equal to sec(cot" (3x)). (You may assume that - < cot (3x) < .) Provide...

A:

Q: 7) sinh 2xdx 8) fcosh vdv 9) f cot ydy pai4 sec? Jwdw

A:

Q: 2. Solve the following differential equations. (a) y' = x2 - xy +1. (Hint: Consider the subsitution ...

A:

Q: A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D(x) = 67...

A: we have to find the elasticity.

Q: (a). Write the distance from point P(, y) on the line y = 2x to the point (3, 3) as a function of c....

A:

Q: Lind ds 6) 5. 52+w²

A: It can be solved using chain rule and divide rule of differentiation.

Q: Determine the total work, by Green's theorem, performed by the force F(x, y) = field, on a particle ...

A:

Q: Approximating Area with the Midpoint Rule In Exercises 67–72, use the Midpoint Rule with n = 4 to ap...

A: Given: f(x)=x2+3Interval:[0,2]n=4

Q: Find the radius of convergence of in=0 negative infinity -1 infinity

A:

Q: If f(t) -Int find f'(t). Use exact values. 4 16' f'(t) = 2 x o tở In(t)

A: This is a problem of differentiation. Please follow the procedure given below. 

Q: Use the given information to determine the values of the remaining five trigonometric functions. (As...

A: Solution ) sin A = 3/5 We know sin2 θ + cos2θ = 1 1)cos θ = √( 1 - sin2θ) cos θ = √( 1 - ( 3/5)2) co...

Q: Find the extreme values of the function f(x) = x3 + 9x² + 5 on the interval x E [-1,3]

A:

Q: Use the quotient rule to find the derivative, h' (x), of the following function. 3x h(x) 8- 5x Provi...

A:

Q: Find the radius of convergence for 2" -(4x–8)" n n=1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Given f(x,y) = 3x sin(3xy). Find fx(3,2). Give you answer correct to two %3D decimal places. Answer:

A: Topic:- partial derivatives