A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s=112t−16t2, where s is the distance from the ground. What is the maximum height reached by the stone?

Q: For the following graph of a function, estimate the area under the curve in the interval [-4, 2]…

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Q: Let f(x) = e2 sin x 1. Use the local linear approximation of f at x = 0 to approximate e2 sin (0.01)…

A: 1.          given is f(x)=e(2sin(x))f(0)=e0       =1f'(x)=2cos(x)e(2sin(x))f'(0)=2linear…

Q: 2. Given the graphs of f(x) and g(x) as shown, find: ✓✓✓✓ a) f(g(0)) b) f(g(2)) 67. -20 -2-

A: f(g(0))=? f(g(2))=?

Q: 7. y' = e² + 2y; y(0) = 2

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: For the questions provided, find the values indicated and solve (using Logarithms where needed) 1.…

A: '

Q: ૩ 3* sech³ (3) 1+tanh (3) S- -dx

A: Substitution method in integration: To simplify the integral, in the given integral independent…

Q: I. Evaluate the following limits. 2 2. lim (x - Inx)* x→0+

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Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables

Q: Evaluate (2x + 3e* - 4) dx a. 12.43 b. 13.45 c. 14.24 d. 15.23 e. NONE OF THE ABOVE A О в Oc O D DE

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Q: Find the derivative of the following functions. g(x)=(x²³-3x²+1) -9x(x-2) (x²-3x²+1)* g'(x)=-

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Q: I can't understand your solution.

A: Let's solve given integral.

Q: y' = xy2 O y(x? + c) -2=0 2 (x² + y=(x+ c) + 2 = 0 y(x= + c) + 2 = 0 y2(x? + c) + 2 = 0 00 Ꮎ

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Q: S 36x2+25 - dx

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Q: Find ди ds if w = sin(xyz), x = 1 - 3t, y=e¹-t, and z = 4t, find o

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Q: √2+x-√2-x X lim- --0

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Q: company

A: Please refer to the image below

Q: PLEASE SHOW COMPLETE SOLUTION.   Find the area bounded by the curve x = y^2 + 2y and the line x =…

A: Area under curve

Q: Solve the differential equation of order one.  (3x − 1)y′ = 6y − 10(3x − 1)1/3

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Q: Q4: Solve the follov A) Find and graph the volume generated by revolving the first quadrant area…

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Q: [x³ In 4x dx A) _ x4nux - A x +C oA nixt dx4+c 4x 16 B) In 4x xr…x4.C D) =xAndx- +x4+C

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Q: Find the area bounded by y = 2x² and y = x a. 9/2 b. 7/2 c. 5/2 d. 3/2 e. NONE OF THE ABOVE

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Q: Perform the following integration. 1. (sinhr) (coth² x + csch³ x) dx sec³ x tan x 2. S dx √2 + sec x…

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Q: Given f(x) = a-1 5xª−1(1 − x)b−¹,0 0. Evaluate ſ*x* f (x)dx. HINT: Express B (a,b) (¹ rk f(x) dx as…

A: Let's evaluate given  expression.

Q: Find the average value of f(x) = -3√x + 5x over the interval [0, 3]. Submit an exact answer using…

A: This question can be solved using the concept of average value of function over an interval.

Q: Prove that d/dx(cos x) = −sin⁡ x using the definition of the derivative.

A: Given: fx=cosx   As we know from the definition of the derivative; The expression for the derivative…

Q: 3. S. 3*sech³ (3³) 1+tanh (3*) -dx

A:

Q: ways

A: Please refer to the image below

Q: Define R as the region bounded by the functions f(x) = 3 and g(x) = x + 1 between x = 0 and x = 1.…

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Q: handwritten. Please skip

A: We assume inf B is the greatest lower bounded of B which means that it is lower bound : inf B ≤x…

Q: To find the distance across a river, a surveyor chooses points A and B. which are x 450 ft apart on…

A: Consider

Q: Whatis the equation of the line that passes through (-3,5) and is parallel to theline 4x - 2y + 2 =…

A: The line passing through -3,5 and parallel to the line 4x-2y+2=0

Q: The choice of u and du is subject to trial and error. Identify the appropriate choice of u and du…

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Q: What is the general solution to the differential equation (tan x)dy - (4y In y - y tan³x)sec²x dx =…

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Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

A:

Q: solve the equation! - A (a) Y'(t) = -Y(t) + sin(t) + cos(t), Y(0) = 1; Y(t) = sin(t) + ce-t. b)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Determine the intervals on which the function is concave up or down and find the points of…

A: Point of inflection is the point where f''(x)=0 A function is concave up in the interval (a,b) if…

Q: v²dx + x(x + v) dv=0 O xv² = c(x+2v) Ox²v² = c(x + v) X V 2 Oxv² = c(2x + v) O xv² = c(x + v)

A:

Q: The population of a municipality in the country varies according to the function…

A: Topic:- Algebra

Q: Find the area bounded by y = sin √x and y = 0 on the interval [0, π^2].

A: The curves are y=sinx, y=0 on the interval 0, π2

Q: 2. Evaluate all of the integrals. 2²-x+4 (x + 1)(x²+2) da

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Q: Calculate the amount of money Cynthia had to deposit in an investment fund growing at an interest…

A: To find out the amount of money that Cynthia has to deposit.

Q: Find the general and the particular solution: d²u du = 4(1 + 3v)²; u = -1,and = -2 when v = -1 dv²…

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation

Q: Stan5 x sec³ x dx

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Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: Let R be the region below bounded by the graphs of C₁: x² + y² = 16, C₂: y = 4 − (x + 2)², and C3: y…

A: If you have any doubt feel free to ask.

Q: Σ(;). Since the series can be rewritten in the form 4 a = r= it is a geometric series with:

A:

Q: Find the area of the region bounded by x = the horizontal strip. y²+1 and the y-axis using

A: Area between x=11+y2, x=0

Q: Given F(x) below, find F'(x). Provide your answer below: F'(x) = 4x F(x) = f** So t t+2

A: Given F(x)=∫04xtt+2dtTo find F'(x):