Type your answers in the following order and format: a=1,b=2. DO NOT include spaces in between characters. * Find the values of a and b for the curve x'y+ay =b if the point (1,1) is on its graph and the tangent line at (1,1) has the equation 4.x+3y=7. Your answer

Q: Find the general solution of (2x – y) dy = 2y – x - da

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Q: Evaluate the following limit: x² + x- 2 lim- x-1x2- 2x + 1 If it does not exist enter DNE. Round to…

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Q: 22 – 9x? = 1 4.

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Q: Find y' if ey+y²=2x. yey – 2 y'= хе + 2у хе + 2у y'= ye – 2 хе*У + 2у y'= 2 – yey 2 – ye y'= хе*У +…

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Q: |x= 8| f (x) = Evaluate the left-hand limit of as X8. 16- 2x O 1/2

A: Given,            fx=x-816-2x as x→8To find : Evaluate the left-hand limit of the given function.

Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: The triangle ABC is defined by the vertices A(1, -2, 2), B(1, 4, 0) and C(-4, 1, 1). Let M be the…

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Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

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Q: Q3) Find the Area bounded by the curves y? = x and x = 2y – y?.

A: The given curves are; y2=x & x=2y-y2   Now find the point of intersection between the curve y2=x…

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: 10 if f(x)= t +P, then %3D f'(X) = f'(-2)=

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Question 3 2 dr sech 2r = A True B) False

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Q: At what rate is the distance between the planes changing? Step 1 Let s denote the distance in miles…

A: Topic:- geometry and application of derivatives

Q: Find f"(2) if Ax) %3D x² - 3* 08 O -7 4 O 2

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Q: Is Rolle's theorem valid for the function f(x) = V1- a. Yes. It is valid in this range b. No. It is…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 9…

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: B. Evaluate the following 1 dx 2. 2 tan(x)dx 3.

A: We have to slove above question

Q: 3. Determine the following a A negative angle in radian measure coterminal to Show calculation steps…

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Q: Problem 2: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt,…

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Q: Q3) Evaluate triple integral f x - y²)dz dy dx.

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Q: is satisfied. Finally, to determine if Rolle's Theorem can be applied, we also need to check if the…

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Q: Consider the solid bounded by the planes: =x+y, z=30, x=0, y=0. Determine the volume of the solid.

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y = dx x² + x – 2

A: Let…

Q: Determine if the following functions are continuous at the given value of x. 1. f(x) = 3x? + 2x + 1…

A: continuty

Q: -2e dx

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Q: Consider the integral 5 x (z° +1) dx. In the following, we will evaluate the integral using two…

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Q: Let 1. f(x) x+1 Use the limit definition of the derivative to find (i) f'(-4) = (ii) f'(- 2) = (i)…

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Q: Find the surface area of the cone z = x² + y2 that lies between the plane y = x and the cylinder y =…

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Q: Question 4 -e-*) dx Evaluate: A '+C 2 B cosh x +C sinh x +C D – sinh x +C E None (F -cosh x +C 2

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Q: Cha invests Php5,000 in an investment that earns 5% per annum. How many complete years does it take…

A: The given problem is solved below in detail.

Q: Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

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Q: Ob.2 amom +C Evaluate +Vrdx Oa.5 2 5 3 2 Oc 2 wn +C Od 3 +C 2/3

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Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: 1 Find "(x) if Ax) -. %3D X+1. 1 (x+1) (x+ 1) -2 (x+ 1)3 12

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Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: Let f be the function defined by ƒ (x) = cos( (/T). (a) Approximate the definite integral| f(x) dx…

A: We have to find the definite integral by using midpoint riemann sum and trapezoidal rule

Q: Find the Area bounded by the curves y² = x and x = 2y – y². %3D

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8

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Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Let a = 2i - 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8

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Q: Step 1 In pert (a), it was found that the two planes were 200 miles apart and getting closer at the…

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Q: 1. S(5x4 + 2x – 1)dx

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Q: 4.) f (x) = %3D x3 5.) f (x) = 2x² + Vx

A: we have to find the differentiation of given function

Q: csc 2 5x cot 5x dx, can be evaluated conveniently using Trigonometric Transformation. ( A) True…

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Q: Evaluate fs 2°ds O a. 2*(sln2 - 1) (In2)2 O b. 2(słn2 - 1) (In2)2 O C. 25 - 1) In2 O d. 2° (+ 1) +1)…

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Q: Which of the following yields the value 3187 (8r+7y)dudy (8r+7y)dydx (8r+7)dudy O none of the oices

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Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: Question For the function given below, which statements concerning Rolle's theorem are true? —3х - 1…

A: This question is related to Rolle's theorem, we will solve it using given information.