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Q: Find the derivative using suitable differentiation rules: + 3x + ¹) J- = 5x + sin(x² + 3x + 1)…

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Q: Find the limit of the rational function (a) as x→∞o and (b) as x→→∞. 6x³ +9 x³x²+x+3 f(x)=

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Q: A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall…

A: A cat falls from a tree at time t = 0. v(t)=-32t ft/s

Q: 2 32 32 0-22 3 y=5x-x2 y = x 1 2 3 4 (4,4) G

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Q: pose f'(x) = √(x+3) and f(1) = 0. Find a formula for f(x) and show all of your work.

A: Given query is to find the function.

Q: J ㅌ ation

A: We have to find the value of the given definite using the given information

Q: f-¹(x) = The domain of f-1(x) is all x f(x) = 6x - 12 13x + 9 be careful with your parentheses in…

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Q: Let f(x) 07 O O 11 - S x² + 1 4x – 1 - if x ≤ 1, Determine the value of (ƒ o f)(1). if x > 1.

A: The answer is in step 2.

Q: Find the dy/dx: y=4/x^3

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Q: Consider the region bounded by the curve y = 27x − x4 and the x-axis.  Find the exact area of the…

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Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti + cos(t)j +…

A: Given; Limt-pi (ti+cos(t)j+sin(t)k).

Q: A particle moves along a line so that its position at any time t > 0 is given by the function; x(t)…

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Q: A particle moves in a straight line with velocity t-2-1 ft/s. Find the total displacement and total…

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Q: Consider the region bounded by the curve y = 4x2 - x3 , the x-axis, and the lines x = 1 and x = 3.…

A: Graph:-

Q: Evaluate the integral using any appropriate algebraic method or trigonometric identity. X X +7 -dx…

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Q: 6. Use Calculus techniques and a calculator to solve this problem. Include explanation of how you…

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Q: Consider the initial value problem y" +36y=et, y(0) = yo, y'(0) Suppose we know that y(t) → 0 as…

A: The given differential equation is: y''+36y=e-t Boundary conditions are: y0=y0  ,y'0=y'0yt→0  as t→∞

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 O A…

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Q: equation of the line that satisfies the given conditions. Through (4, 7); parallel to the line…

A: Given query is to find the equation of the line.

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

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Q: A graphing calculator is recommended. The displacement (in centimeters) of a particle s moving back…

A: NOTE: Refresh your page if you can't see any equations. . the given position function is

Q: Use regression to find an exponential equation that best fits the data above. The equation has form…

A: use the calculator to find the exponential regression in your calculator press STAT select edit by…

Q: 1. A chord passing through the focus of x²= 8y has one end at the point (-8,8). What is the other…

A: As per our guideline we can solve maximum one question you can repost other question

Q: Solve the exponential equation by expressing each side as a power of the same base and then equating…

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Q: The Cartesian coordinates of a point are given. (a) (-2,2) (1) Find polar coordinates (r, 0) of the…

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Q: At what points is the function y = X +8 x² - 15x + 56 continuous?

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Q: A woman is on a lake in a rowboat located one mile from the closest point P of a straight shoreline.…

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Q: -1 tan¹ n n

A: NOTE: Refresh your page if you can't see any equations. . find the limit of the sequence

Q: If z² = x³ + y²₁ dt dx dt Please give an exact answer. || - Provide your answer below: - dy 2, = =…

A: Topic = Derivative

Q: Let r(t) (4t+2, -4e¹, 2e #¹). Find the line (L) tangent to r(t) at t = 3. L: (x, y, z) = = +t

A: Given vector:- r→t=4t+2,-4et,2e-4t

Q: If g(x) = 5 +x+2e², find g-¹(7) = 1

A: NOTE: Refresh your page if you can't see any equations. . here we need to solve this equation using…

Q: Consider the function h(x) = f(x² - 1). Give the formula for the derivative h'(x).

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Q: Consider the function h(x) = (x+1)f(x). Give the formula for the derivative h'(x). 1

A: Given query is to find the derivative.

Q: Find the remainder: (3x² + 16x − 2) ÷ (x + 5) 0 O 153

A: Given        (3x2 + 16x - 2)÷(x + 5)  Here we have to find the remainder.

Q: How did you get the rewrite from sin^2(x)/sqrt(1+cos(x))

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Q: The sum of four times a number and 1 more than the number is the same as the difference between −27…

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Q: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = t³ - 3t² 1.…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter ()+8², ti T(1) -

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Q: Differentiate f(x)= In(sin^2 x). f'(x)=? Please answer ASAP and write neatly thank you.

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Q: Let F(t) = (4t¹ +4, t² − 4t³, 2tª). Find the line (L) tangent to r(t) at the point (68, 36, 32) L:…

A: Given vector:- r→t=4t4+4,t2-4t3,2t4

Q: A particle moves along a hyperbola xy = 12. As it reaches the point (4, 3), the y-coordinate is…

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Q: Consider the following equations. f(x) √x + 3 1 g(x) +3 Sketch the region bounded by the graphs of…

A: Let's sketch the graph of functions and find area.

Q: Multiply and simplify: (4x) (7x²) The answer can be written in the form cxº where: C = p=

A: Simplify

Q: If f(x) = x³ + 6x +5, find (ƒ−¹)'(5) =

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Q: ans against the side of a house. The angle of elevation of the ladder is 66°, and the top of the…

A: Given query is to find the length of the ladder.

Q: The differential equation (5y - 2x)y' - 2y = 0 is a) Exact b) Non-exact The differential equation xy…

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

Q: 7 Newton's laws of cooling proposes that the rate of change of temperature is proportional to the…

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Q: Consider the differential equation y" - 25y = 25x e-5z Use coefficients c₁ and ₂ if needed. Use…

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, write the…

Q: If g(x, y) = x2 + y2 − 6x, find the gradient vector ∇g(1, 4) and use it to find the tangent line to…

A: Concept: Gradient of function g(x, y) ∇g(x,y)=∂g∂x,∂g∂y Equation of the tangent line at g at point…

Q: แบบฝึกหัดที่ 1 สูตร m=slope = f'(x₁) - lim m=slope = f'(x) - lim สมการเส้นตรง y = mx+c 15 HO X x-2 3…

A: Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If…