dy Find given x'+y' =8xy. dx Note: Enclose all terms in a parenthesis if either the numerator or denominator contains more than one term.

Q: Given the function: f(x,y) = 4x*y² – 10p +y , find f a. 16x'y-60xy O b. 48x°y O C. 16xy – 10y O d.…

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Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

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 x and x = 2y – y².

A: Topic = Area Area bounded by curves is 13.

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

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Q: Express the shaded area of the region shown below by double integrals of order of integration (1)…

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

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Q: Question 2 Evaluate: J y* sech (e m)tanh (e ) dy A sech (y7) + C B) None © -eh*(,) + C E

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Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: Consider Evaluate 3x)

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

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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: 1 Find f'(-1) if Ax) = (2x + 1)², O-4 04 O-1

A: The given function,       fx=12x+12

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Use the appropriate Product Rule to evaluate the derivative, where ri(t) = (9t, -10, -t°),r2(t) =…

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of ¡ does the curve has…

A: The given parametric equation is x=3+5t, y=1+3t The curve length is 34 Let the value of t is t1 to…

Q: Find the saddle pointis of the function f(x,y) = x° +y°+i y+4 Oa(5-1) Oc (4.0) & (4,0) Od(0.0)

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Q: Since f'(c) f(1) – (0) f(1) – f(0) = 1, f(c) = 1. We therefore equate f'(x) to 1 and solve for x.…

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Q: Determine a and b so that the function f(x) is continuous for all values of x. jika x <- 2 sin x…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Find all values of x that satisfy the equation f'(x) = g'(x) if f(x)=sin x and g(x)=cos x. a. * +kT,…

A: Given that     f(x) = sinx and g(x) = cosx  Here we have to find all the values of x that satisfy…

Q: Descibe he moton of a partice with position y= 5 sin t; y=2 cos t as t varies in the interval - T, 5…

A: To find the motion of particle.

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

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Q: The limit represents a derivative f'(a). Find f and a. V3 sin (5 + h) lim 2 h→0 h (Express numbers…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x2 + 16

A: We will use simple Integration rules to solve this question.

Q: g"(x) sin(x- 1) x-1 -4 13 A(x) = kr -8x + 6, -1 10 x>3 8 3 -1 (E) Find all x value(s) on the open…

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Q: find the derivative and simplify the answer sin² (esin t) + cos-{(2t3 – 5)

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

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Q: f(x) – f(2) x - 2 Find the difference quotient when f(x) = 2 + 4x + 5x². Simplify the expression…

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Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

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Q: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

Q: A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box…

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

A: Draw the graphs of the given curves and mark the intersection area.

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: Let's find.

Q: xist enter DNE.

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: 2x 4. Given the function F (x)= 3 do the following: 4.x +1 a. Find F-1 (x). b. Find dom F and dom…

A: Given,            The function is Fx=2x-34x+1.

Q: Use the limit definition to compute the derivative of the function f(t) = , at t = -4. (Use symbolic…

A: This question can be solved using the concept of limit definition of derivative and equation of…

Q: 8. (a) Use the limit comparison test to determine whether the series converges. k=1 (b) Use the…

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Q: Find dy for the following functions (メ+リ)+(メーツ)ニxャガ 4.

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Q: Descibe the level curves of the surface f(x.y)=x-4y. O a Hyperbolas Ob.Parabolas Oc Crdes Od Elipes

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Q: Cara tosses a pair of equally weighted coins 4000 times, and two heads appear 40 times. What is the…

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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: 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: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: The limit below represents the derivative of some function f(x) at some number a. 3(3 + h) - 243 lim…

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Q: cos 2x sin'x dx can be evaluated by factoring sin x as (sin?x) 2sinx and transform sin?x into 1-…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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