465.98 23.98 2.789 56.09 ATATA TTA TA

Q: 4. Using logarithmic differentiation, or otherwise, find the derivative of y = (sin r)".

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Q: Solve for k such that 1 | k(x² – 2x + 1)dx = 5

A: Given problem:- ∫ k(x2 -2x+1) dx =5  Solve for k

Q: If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a…

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Q: Solve the differential equation Integrating Factor by Inspection: (2y – 3x)dx + xdy = 0

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Q: Given the function f(x) = Which f the following is/are true? (x- 1)(x + 1) 1. lim f(x) = +00 2-1+ 2.…

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Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

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Q: Describe the graph of the equation. r= (5 - 31) i - 10:j O tis a line in 2-space that goes through…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: 2. dy dx

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t++o \ 5t2 + 6' 5t (0,0)

A: Simplify the component wise

Q: r=5 sin  18t  i−5 cos  18t  jr=5⁢ sin⁢  18⁢t⁢  i-5⁢ cos⁢ ⁢ 18⁢t⁢  ⁢j It is a circle of radius 1818…

A: We have to find the centre and radius of the circle.

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = e"i+ e*j к(t)

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Q: Exercises Distinct Real Roots of Auxiliary Equation Find the general solution 5. (D² – 1)y = 0

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Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

A: Let the first number be 'x' second number be 'y'. A/q  x+5y=50⇒5y=50-x⇒y=50-x5 The product of first…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise p…

A: As we know that; The Green's theorem; ∫CPdx+Qdy=∫∫D∂Q∂x-∂P∂ydA   Given: I=∫C3xy dx+6xy dy And C:…

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

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Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: Without evaluating the constants, the partial fraction decomposition of 7x3 – 11 (4x3 + 7x2 +…

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Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A: This question is related to vectors, we will solve it using given information.

Q: Using appropriate substitut tan³x dx sec5x is equal to

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x?y – 6xyz + 10yz2…

A: Given problem:- Find the first partial derivatives with respect to x, y, and z.   f(x, y, z) = 4x²y…

Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: A differential equation is considered to be ordinary itit has one independent variable None of the…

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Q: 3. A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: d Caleulate fri(t) - r(t)] and ri(e) x ra(t)] first by differentiating the product directly and then…

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: 1.) Find the area bounded by the curve y?= 1 - x and 2y = x + 2 2.) Find the area bounded by the…

A: Solution is given below:

Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) = to find «(t). r(t) = t’i + t°j %3D 126 t5 K(t) (4+…

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Q: Find r'(t), r"(t), r'(t) •r"(t), and r'(t) x r'"(t). r(t) %=D 흑래- 26j + 하하k (a) r'(t) (b) r"(t) (c)…

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Q: The linear system with corresponding augmented matrix 2 -1|4 is consistent. True False « Previous…

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Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 <ts 1. / (x+ 3y²) dy #4

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Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

A: A detailed solution is given below

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (7, 5, 1.386) x(t) =…

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Q: Find the partial derivatives of f (x, y) = 5x°y². %3D (a) fa(x,y) = (b) fy(x, y) (c) fa(3, y) = %3D

A: ∂xn∂x=nxn-1

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

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Q: Find div F and curl F if F(x, y, z) = x*i – 5j + yzk. - div F= curl F=

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Q: 21. Solve the equation y' = (x²+ 7) / 9 (2x / 9) + c b. y = (x / 18) + c 22. Solve the equation y' =…

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Q: nd the general solution of the following: 2. (D3 – 4D² + 4D)y = 0 3. (4D2 – 6D + 1)y = 0 4. (25D2 –…

A: Topic:- differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: Using appropriate substitution | sec*x dx is equal to In|secx + tan x| -1 + C 2cos?x + sec x tan x +…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

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Q: ydx — хdу %3D у?dy

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). r(t) = ti + t°j

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: x 1 What is lim f(x)? x→-1 O 3 O 4 O 2

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Q: Verify Green's Theorem by evaluating both integrals y² dk + x² dy = / dA ay ax for the given path.…

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Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: 8 – a? if – 2 2 between O 8 and 16 O O and 8 O 16 and 24 O 16 and 33

A: Given problem:-

Q: f 1 1 3. The graphs of f(x) and g(x) are given above. Find the following: (i) S'(1), where S(x) =…

A: Differentiation

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t3i + 14tj – 6/tk) dt

A: we have to find the indefinite integral