- 13. If u = (4, -9, -1) and v = 4ỉ − 2] + k, determine each of the following: a. u.v f. (2ū+ v) × (u-2v)

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32) sin(t)dt

A: The tabular integration is a process of evaluating the integral using integration by parts. In this…

Q: 2. Determine the area above f(x) = 3x² + 6x - 9 and below the x-axis.

A:

Q: Determine the cardinality of each of the following sets. a. A x B, where A = {a, b, c, d, e}, B…

A: a) A=a,b,c,d,e, B=xb) a,b,cc) d) Φ,Φ,Φ,a,

Q: Find a function p(x) defined by a polynomial of degree 3 with a real coefficient that satisfies the…

A:

Q: Determine the exact value of the following trigonometric functions given that cos (0) radians lies…

A: Given  cosθ=-96104  .............(1)θ is in radian and lies in the 3rd quadrant.

Q: (B): Find the integration by using substitution method [x√2x - 1 dx

A:

Q: dy -2x² + 5y5 + ey = 0. Compute in terms of x and y. dx Let y(x) be defined implicitly by G(x, y(x))…

A: We have to find derivative

Q: C. Find the volume of the solid generated by revolving the area bounded by the given curves about…

A:

Q: Find the derivative of the function. g(x) = ((7x^2-4)/(4x+7)^-2

A: We have to find the derivative

Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

A:

Q: Evaluate 1 dx (x - 2)³

A: we have to solve the integration

Q: Find the area of a parallelogram having the vertices P(1, 1, -1), Q(4, 2, 1), and R(6,3,1) O √13 O…

A: To find the area of a parallelogram having the vertices P1, 1, -1, Q4, 2, 1 and R6, 3, 1.

Q: Determine the arc length of the curve formed by the polar equation r = 4 cos 0 - 4. 2T 2п 2√/2 √1 -…

A:

Q: (b) n 1+ (x-1)"; r=1/e Σ(1-1) η n=1

A: Here, the given series is: ∑n=1∞1+1nn2(x-1)n Let, an=1+1nn2(x-1)n; n≥1

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t + 32) sin(t)dt

A: We can evaluate the given integral by using the tabular integration.

Q: (c) an = (-1)". 2n n!

A:

Q: 1 (2m-3)√4m (m-3) dm ans=1 arcsec( ² m - 1) + C

A:

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+ 32)sin(t)dt

A:

Q: its not 1

A:

Q: (1+x² +C B [2x (1+x) dx-A)- 11 10 11 f(x)=x+cosx, xe [0,7), then the function has an inflection…

A: from graph  stationary point: point of function is a point where the derivative is equal to zero .…

Q: 7. S d.x 25x²+36

A:

Q: Consider Mean Value theorem for derivative for function f(x) 4(1-2x) in interval [0,1]. TCOS(TX) -

A:

Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32)sin(t)dt

A:

Q: Find the tangent line approximation for √1 + x near x = = 5. ||

A:

Q: Find the area of the region bounded by y = 9 – x^2 and y = x^4

A: Let's find area of the region bounded by given two curves.

Q: 6. S e3w dw 9-4e6w

A:

Q: Solve the following integrals. 3.) S fafy dxdy y²-x²

A: On solving this we will get

Q: T 4.) x² sin(xy) dydx

A: Solve the following integrals.        ∫0π∫01x2sin(xy) dydx

Q: Show tha

A:

Q: Applications

A:

Q: Find the Fourier series for the periodic extension given below: 1, x(t) = t = [0,2] te [2,4] (-1,

A:

Q: Find the point of intersection. 4₁:X-17 y-58 z-23 3 2 = 11 L2 x-49 7 N y-26 4 =z-15

A:

Q: Find the area of the shaded region. f(x) = 10x - 3x²-x³, g(x) = 0 The area is (Type an integer or a…

A: This question can be solved using the concept of  area bounded by two curves.

Q: A rectangular field as shown is to be bounded by a fence. If fencing is not needed along the river…

A:

Q: seconds after the start of the movement. (B) Use Tabular integration to evaluate the following: -…

A: Let's evaluate given integral by using tabular method.

Q: Q2: (A) Show that if y=csc(u), then dy du -csc(u) cot(u) dx dx

A: follow next step

Q: PART I. Calculating First Order Partial Derivatives 1. f(x, y) = 2x² - 3y - 4 3. f(x, y) = (x² -…

A:

Q: Consider the following pattern 9 * 1 - 1 equals 8 9 * 21 - 1 equals 188 9 * 321 - 1 equals 2888 9 *…

A: Concept: Inductive reasoning: Inductive reasoning is an approach for arriving at inferences by…

Q: Question 8 (a) Find the following integrals: 1 (1) √4x²+0 d 6 (ii) -dx -2x-8

A: (i). Given: I=∫14x2+9dx   ...1   As we know that; The trigonometric identity; 1). tan2x+1=sec2x 2).…

Q: Find the first derivative of y = (e³x)(3x² – 7)

A: This question is related to differentiation, We will solve it using given information.

Q: 2 ( D° _ 2D - 20 - 3D - 2) y = 0 = 9

A:

Q: Q2: dy du (A) Show that if y=csc(u), then -csc(u) cot(u) dx dx

A: SOLUTION-

Q: Find the area bounded by y Round to four decimal places. 3 144 - 9x² X = 0, y = 0, x = 2.

A: SOLUTION-

Q: 3-Given the points A(4, 7, -2) and B(-2, 1, 6): a) Find AB and express AB in terms of i, j,K.?(..

A:

Q: Evaluate the following integral: * *π/2 [sin² 6 1/42 4 O - (2/63) O - (3/28) O 2/63 sin x cos³ x

A: The objective of the question is evaluate the definite integral and choose the correct option.

Q: If you are not given the graph of a cosine function f(x) however its maximum and minimum are 3π…

A:

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

A:

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Find the direction cosines of the vector (4,-8,-8) 8 8 O cosa = 4 12 cosß cosy= 12 12 8 cosa = √12…

A:

Q: Find closed Sets A= [2,5), B = {2, 4, 6, 8, 10,--- }, C = {6, 21, 42, 58}

A: We have to find the closed sets.