Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i + 3t²j, t= 1

Q: 1. Consider the region bounded by y = x and y = Vx, shown below. Find the volume of the solid obtain...

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Q: 3ysinxdx/dy-2xycosx=0, Find exact differential equations

A: Given  3ysinxdx/dy-2xycosx=0

Q: The limit represents a derivative f' (a). Determine f (x) and a. 6h lim h 1 h-0 (Express numbers in ...

A: find fx and alimh→06h-1h

Q: Evaluate the integral. 1 2187 19683 3e° 2187 e 4

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Q: 2 Can the Fundamental Theorem of Calculus be used to find /. L dx? 6-x 6-x O Yes, f(x) = is continuo...

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Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt    

Q: State the property presented 10 + (4 + 11) = 10 + (11 + 4) a. commutative property b. associative...

A: Here is given that  10+(4+11)=10+(11+4)

Q: x* + x³ + x² – x + 1 – x + 1 x(x² + 1)²

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Q: B2/for the figure below find. (a) Total shaded Area : * Y 3 cm y3kx2 8 cm 7 cm 6 cm

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Q: Sketch the region enclosed by a + y = 6 and æ + y= 0. Decide whether to integrate with respect to a ...

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Q: What value(s) of o are an appropriate choice when proving the following limit? lim (2 + 9x + 25) = 5...

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Q: Find the slope of the normal line y^2=1-x^2 at point (2,1)

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Q: Find the volume of the solid formed by rotating the region enclosed by y = e + 3, y = 0, x = 0, z = ...

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Q: Given the geometric sequence: 36, 120, 400, ... Find an explicit formula for an, where the first ter...

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Q: a population of 7.2 million grows at a constant percentage rate.  1. what is the population 1 centu...

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Q: 7. Consider the region above the r-axis and below y = e-² with x > 1, shown below. 4 Consider a wiza...

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Q: 4. A certain computer algorithm used to solve very complicated differential equations uses an iterat...

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Q: From the graph of f, indicate the intervals on which f is continuous. 2 4 -8

A: The graph of a function f is said to be continuous in an interval if the graph runs continuously wit...

Q: Differential Operator General Solution DN AxN-1 + BxN-2 +..+C (D - a)N AxN-leax + BxN-2eax + ... (D?...

A: differential equations

Q: 16x2 - 25 -da Evaluate the integral: 23 (A) Which trig substitution is correct for this integral? O ...

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Q: C 1000 A В

A:  We know that law of sine is : SinA/a = SinB/b = SinC/c. Here A,B,C are angle of triangle and a,b,c ...

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 + 3xy...

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Q: The given problems need the first derivative. Find the first derivative. y = 3x + 6 y = x2 –1

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Q: 3. (a) Evaluate the following with the trigonometric form of Beta functions(Give your answer in term...

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Q: Find all the values of a such that the given series would converge. (– 1)"9"x" Σ n=1 (Vn+ 5) The ser...

A: Here we have to find the values of x such that the given series would converge.

Q: (x² +3y² +5)dx +(6xy+ 6y+3)dy = 0 Identify the exactness of the differential equation. Calculate the...

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Q: Use the graph to find the limit (if it exists). Sx + 3, x + -1.5 lim f(x), where f(x) = { -3 ,x = -1...

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Q: Tell whether each given function has a solution on the indicated closed interval. Prove using the IV...

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Q: Q2 Second-order non-homogeneous ordinary differential equation given as; y" + 3y' –10y = e2x Calcula...

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Q: f(x,y) = 100x062y0 38. Find the marginal productivity of labor and capital.

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Q: The following statements are true EXCEPT A. lim x →2 x²=4 B. lim  x →-2 x=-2 C. lim x →-2 x³=8 D...

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Q: 4. if x - 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = lim...

A: Topic = Limits

Q: Vx+3 4. f(x) = **3 f'(1) x-4

A: Given:- f(x) = √(x+3)/(x-4)  To find:- f'(1) 

Q: (b) Given the first-order differential equation as below: (x² +3y² +5)dx+(6xy +6y+3)dy = 0 (i) Ident...

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Q: Differential Operator General Solution ... DN AxN-1 + BxN-2 + ..+C (D - a)N AxN-leax + BxN-2eax +.. ...

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Q: 4. (a) Prove the reduction formula: tan?n-1 (2r) _ [ tann-2 (2r) dr 4n- 2 tan" (2.r) dr (b) The redu...

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y ...

A: Solve the curve by using cylindrical shell method.

Q: Find all the second-order partial derivatives of the function f(x,y) = 4x2 + 9y + 7x2y?.

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Q: Which of the following is not in the domain of cot(x)? Select all correct answers. Select all that a...

A: We can answer the question as below.

Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

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Q: (x)

A: We will find the correct answer. 

Q: If Sf(x)dx = 5, i f(x)dx = 2, and Sif(x) dx = -1, find f(x)dx. %3D %3D А.) -2 В.) 2 С.) -3 D.) 3

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Q: дт ду д dy at az az & as Calculate by first finding & and using the chain rule. at as' as' at

A: Follow the procedure given below.

Q: 31, 32, 33, and 34 Use the Squeeze Theorem to find the limit. 31. lim xy sin (æ, y)→(0, 0) x2 + y²

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Q: Use the Chain Rule to evaluate the partial derivative at the point (u, v) = (0,5), where g(x, y) = x...

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Q: 4. Summation of two variables: E(x, +y;)=E×, +£v, i-1 Example Evaluate the following given that x, =...

A: We can find the answers as below.

Q: Vx+3 4. f(x) = f'(1) x-4

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

Q: Given the series: ΣΗ 1 k +1 does this series converge or diverge? O diverges O converges If the seri...

A: Terms of a telescoping series will cancel each other except 2 terms in the series.

Q: 3. The fuel used by a car is defined by f(x)=3x=/80-6x+245. where x is the travelling speed in km/h....

A: The fuel used by the car is given by the function: f(x)=310x2-6x+245 where x is the speed of the car...

Q: For the function f(x,y) = 3x2 + 7y2, find the following. f(x +h,y) – f(x,y) а.

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