Verify the identity. 1 sin² y M 1 1-sin² y tan² y + 1 Use a Pythagorean Identity in the denominator, and then use a Reciprocal Identity. 1 = 1.0 Use a Pythagorean Identity.

Q: ketch the points p/2, 3, 34,4/2,3,1-3 and R (-2,3, 2)

A:

Q: Find dy/dx for the following functions:- u² (4) y=²+1 , u = 3x² - 2 (3) 4x² + 3xy - xy² = 0

A: We can find the answers in the below steps

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

A:

Q: Find the first six terms of the recursive sequence. a₁ = 1, an+1 = 3 - an a₁ a2 = a3 = a4 = a5 = a6…

A:

Q: Given the integral from 0 to x of the function e-x^2dx: Find the summation form of its Maclaurin…

A:

Q: (b) Let f(x)=√x and g(x) = 2x+5, find: (1)fog(x) (2)gof(x)

A:

Q: 2. What is the average rate of change from x = 4 to 9 of f(x) = 200e-03x

A: We need to find average rate of change.

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

A:

Q: In Exercises 5–8, determine whether the graph of the function is symmetric about the y-axis, the…

A:

Q: Use one or more logarithm identities to show that In (2) In(x) for any > Use one or more logarithm…

A: we have to do as per the question.

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: Show the complete solutions. Family of horizontal parabolas whose h to k ratio is 2. Ans: 2xy" -…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The point P(1, 0) lies on the curve y = sin( (a) If Q is the point (x, sin(¹3″ )), find the slope of…

A:

Q: Solve the differential equation by separation of variables: (x²+4) dy + x²y²dx=0 Ⓒ 1 y There is no…

A:

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B.

A: The given vectors A=3i+j+4k, B=2i-3j-k we have to find the vector normal to A and in plane of A and…

Q: 3 2. f(t) = (2t-1)-²; ƒ(1), ƒ(5), ƒ(13)

A: Given function is f(t)=(2t-1)-32 We need to find its value at, f(1), f(5), f(13)

Q: 25. lim h→0 (x+h)² +4(x+h) —x²− 4 at h (A) x³ + x4 (B) x² + 4x (C) 2x+4 (D) nonexistent

A:

Q: Calculate, to four decimal places, the first ten terms of the sequence. 3n 1 + 4n an =

A: Given, an=3n1+4n

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: Given problem:- Differential equation of family of circles centerd at the line y=2x

Q: 53. I 0 f(x) f'(x) g(x) g(x) (A) 15 (B) 3 (C) 2 (D) -5 4 1/1/13 2 - 2 32 3339 The table above gives…

A:

Q: 2+2x-1 dx x³-x

A:

Q: So 1 x²+7x+10 A. B. C. D. 3ln 2-ln 2 3 3ln 2+ln 2 3 3ln 2-ln 2 5 3ln 3-ln 2 3 dx

A: The given integral, ∫011x2+7x+10dx use the integral formula, ∫dxx=ln x+C

Q: A. by extracting square roots. 1. x2 = 169 4. (x - 2)² = 16

A: Answer (4) We have to solve by extracting square roots (x - 2)2  = 16

Q: Find the standard form of a circle given the following conditions. Sketch the graph. 1. x²+y²-25=0…

A:

Q: Integrate on both sides of the equation. 3 y 1+2y dy X 2 dx

A:

Q: 4. 2y2 +8y - 10= 0

A: Given problem:- 4.   2y2+8y-10=0

Q: List the x values of the discontinuities of the function below: y = In (tan²(x)) over the interval…

A:

Q: Write the interval of continuity for the function below: sin(x)√81-x2 x²+x-6 f(x) -

A:

Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

A:

Q: Prove that: B(x+1; y ) + B (x,y+1)= B(x,y) let (x + 1) = X(X)

A:

Q: 1. fx² sec x³ tan x³ dx

A:

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.

Q: integral: 24x² √64 – x² dx

A: ∫ 24x264-x2dx

Q: Solve the Differential Equation x² (y² +3) y(x³+1) dy + dx = 0

A:

Q: Prove the identity. sin (x-y) cosx cosy tan.x - tany Note that each Statement must be based on a…

A: We can prove the given statement as per the example in the below steps.

Q: Test for homogeneity 3. f(x, y) = tanx - sec²x - cosy 4. f(x, y): x²+3xy

A:

Q: Financial planners suggest a monthly budget similar to that shown in the pie chart below.1 Use the…

A:

Q: 6 - x - x² if x ≤ 1 if x > 1 2x - 9 Calculate the following limits. Enter "DNE" if the limit does…

A: f(x)=  6-x-x2    if x≤1 2x-9         if  x>1

Q: Q2: Find dy/dx for the following functions:- (1) y = x³ Inx (2) y=√sinh √tan x (4) y=u=3x²-2 (3) 4x²…

A: As per guidelines we can answer only three subpart questions at a time, so if you need more answers…

Q: 3. Using the following table, find the average rate of change from x = 2 to 11 X f(x) -1 -4 2 4 4 8…

A:

Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xdy +…

A:

Q: So 1 x²+7x+10 3ln 2-ln 2 dx

A:

Q: B. Find the DE of each of the following by eliminating arbitrary constants. Reduce your final answer…

A: Let's eliminate the arbitrary constant.

Q: Find the Differential Equation of the Family of Ellipses with its center at the origin.

A: Here is the solution:

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

Q: 4. Given f(x) = x² +3 and g(x) = -3x + 11, find the following a. f(g(3))

A: Concept: Composition of function: A function is composed when two functions, f and g, are used to…

Q: 29. If a factory continuously dumps pollutants into a river at the rate of tons per day, then the √t…

A:

Q: Question The base formed by slicing through the center of a solid S is the ellipse+ = 1. The cross…

A:

Q: Write the interval of continuity for the function below: tan(cos(x)) log6 (7) f(x) = for 0x< 2π

A: The given function is: f(x)=tan(cos(x))log6xπ

Q: 1. Calculate the following limit analytically or show that the limit does not exist. Re- member to…

A: