lin x→ Sin 2021x Sin 20222

Q: 7.Find of z = 2x³-5xy² 8²z xy

A: topic- partial differentiation

Q: List the first five terms of the sequence. - 1. a₁ = 2, a₂ = 1, an+1 = an an-1

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Q: Find the slope of the tangent line to the graph of the given function at the given value of x. y =…

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Q: et Lim x-0 +e³-x²-2 sin² x-x²

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Q: The function 5x+1 f(x) 1-In (x³ +e) has a Maclaurin Expansion O false O true

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim: x3+4x+3…

A: topic- limits

Q: 2 √z T Evaluate the integral SSS (² cos ²0 +2²) r de dr dz. 000 ▪▪▪ The value is (Type an exact…

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Q: 7- Find fx³√3 - 2x² dx

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Q: Consider - 9 dx. Using rationalizing substitution, we let z = √√e*-9. √√e²-96 What will be the form…

A: The integration of the integral is √(ex-9).

Q: Evaluate the double integral over the given region R. xy² dA 2 X + 1 R xy² SS. dA= +1 R (Type an…

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Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: Using an appropriate substitution | tan³x sec7xdx is equal to

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Q: Sinzo + Cos20 +1 Sinzo- Cos2© +1 - - сото

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Q: Given [ƒ(x) dx = -5, and g(x)= {x²-1,0≤x≤3 . Using the properties of (3x+2 ,3≤x≤5 integral. Find the…

A: Ans= -20  For detail...go through the solution...I have solved using given information in detail

Q: 14. The vectors a and b are given below. Use these vectors to sketch each of the following. za + b…

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Q: (d) √ ² (3 (3 − z)(3z + 1) dz. 0

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Q: height (feet) of a ball launched in the air t seconds after it is launched is given by: f(t)= - 16t²…

A: Velocity

Q: MY NOTES ASK YOUR TEACHER The rate of change of the function f(x) = sin(x) + csc(x) is given by the…

A: Verify the identity

Q: 1. Use the properties of sigma notation and the summation formulas to evaluate 138 540 136 925 10 WI

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Q: Calculus optimisation problem Amount of fuel 'F' (in litres) required per hour to propell his…

A: Given, F(u) is the fuel in liters required per hour. u is the speed in kn/hr u(max)= 40 km/hr F(u)=…

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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Q: Let w=x² +3y² + 2z² where x=rcos, y=rsin 0,z=5t find dw dw ar' at

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Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: Find the unit normal to the surface z=2+2z^2-3y^3 at the point (1,-1,7), pointing down with respect…

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Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

Q: 4. Given z = x-y, Find az/ax x+y

A: Given z=x-yx+y

Q: Let f(x) = In(64x2 + 16x + 26). (If an answer does not exist, enter DNE.) (a) Find the interval(s)…

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Q: Find the cross product a × b. a = (9, 0, -4), b = (0, 8, 0) Verify that it is orthogonal to both a…

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Q: Find Hence evaluate d dr 1 Š S ₁ (1 +2²2)³/26 0 -1 1+x², dx.

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Q: Set up the definite integral required to find the area of the region between the graph of y = 14-2²…

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Q: 15. The sides of a triangle have lengths x, x + 4, and 20. Specify those values of x for which the…

A: Concept: Parallelogram Properties: A Parallelogram is a particular polygon formed by a quadrilateral…

Q: estion 28 Find the next term of the sequence: 243, 81, 27, .... A Moving to another question will…

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Q: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: Find by implicit differentiation, given that x²y - 2y4 = -4. Your answer could involve both x and y.…

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: 1. Determine the value of a such that lim 24-2 Hint: Apply one of the Limit Laws. 3x² + ax + a +3…

A: We have to find limit

Q: The median weight of a boy whose age is between 0 and 36 months can be approximated by the function…

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Q: N A cylindrical tank is filled with gasoline with weight density of 7840 Determine the force exerted…

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Q: There are two extremely important sequences that we will discuss in this chapter: arithmetic…

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Q: Find the domain of the function. (Enter your answer using interval notation.) g(t) = √√√7 - t-√√3+t…

A: For square root function to be defined the term in the square root should be positive

Q: Compute. 13 Σκ k k = 0

A: We have to find out  sum

Q: Water is leaking out of an inverted conical tank at a rate of 8100 cubic centimeters per min at the…

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Q: Evaluate LS ²² s 0 sin z6 dx dy dz

A: In this question we have to solve Triple Integration.

Q: Verify that * ox af dy 2+ ?х ду ду дх ах 22+ 21 ?х ду ду дж 11 olems) for f(x, y)=5x®y -7xy5.

A: Here is the solution of the given problem.  Partial Derivatives.

Q: Numerical Integration: 2 1 Jo √x 1. =dx

A: We can find the answer as below

Q: Find an equation of the tangent line to the graph of the equation 6x - 5x8y7 = 36e6y at the point…

A: In this question, we will compute the equation of the tangent line of the given curve.

Q: Evaluate x + 2 S -dx using rationalizing substitution. Which of the following statements is correct?…

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