y = 1 1+ u 1 1-x

Q: ) Find the area of the region bounded by y = ex, the x-axis and the y-axis.

A:

Q: Evaluate the following integrals 2x ·S- -dx 2 5+2x+x

A: We know that ∫duu = lnu+C ∫1v2+a2dv = 1a·tan-1va+C

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: II. Evaluate the following integrals. 2. f (sin³x)√1 + cos x dx 플

A:

Q: A curve with polar equation r = represents a line. Write this line in the given Cartesian form. y =…

A:

Q: Evaluate the indefinite integral given below using the indicated substitution. /-20 -2(-2x +9)³ dx u…

A:

Q: Q2/ Find the derivative of each of the following functions:- X 2. log₂ x y = X 1+ tan x 1. y=(sin…

A:

Q: Find the average value of f(x) = -3√x+ 5x over the interval [0, 3]. Submit an exact answer using…

A:

Q: 2. 0 sec³ x tan x √2+ sec x dx

A:

Q: Evaluate f(x³ -x + 1) dx a. 0.250 b. 0.500 c. 0.625 d. 0.750 e. NONE OF THE ABOVE

A:

Q: Which statement is true for a function f(x)? b The average value of a function is [ f(x) dx. a f…

A:

Q: I. Evaluate the following limits. sinh x? – r 1. lim r→0 sinhr — -

A:

Q: . Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of…

A: We need to find hyperbola equation.

Q: Determine the instantaneous rate of change of the function f(x) = [x² si sin (2¹) 1+√t x3 At x=1 dt

A:

Q: I. Evaluate the following limits. 1. lim sinh r → r r→0 sinhr – r

A:

Q: lim (sech 2x)csch x x² +0+*

A:

Q: I. Evaluate the following limits x-tanx 1. lim x-sinx x-0

A:

Q: Q2/ Find the derivative 1. sin(xy)= of each of the following functions:- 2. y =(Inx)³ 3. y=cos (sin…

A:

Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: Find the area bounded by y = sin √x and y = 0 on the interval [0, π^2].

A: The curves are y=sinx, y=0 on the interval 0, π2

Q: 0 sinx + 2cosx dx

A:

Q: Test for exactness then solve. (1 +  y2)dx + (x2y + y)dy = 0

A:

Q: 5- A. 3. C. +X+ P 上一站 -- V -4x 一 --年 -c + c -c

A: Topic:- integration  Note :- as per our guideline if more than one question uploaded than only first…

Q: २ -2 el dy ely +2 e. 2

A: To integrate.

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

Q: Evaluate the following integrals. 9x - 5 4. J dx 9x² 18x + 13

A: Given ∫9x-59x2-18x+13dx   Let  9x-5=αddx9x2-18x+13+β i.e.,    9x-5=α18x-18+β…

Q: A group of management students are creating a business plan for their proposed shoe brand…

A: Given problem:- A group of management students are creating a business plan for their proposed shoe…

Q: √2+x-√2-x X lim- --0

A:

Q: 5x4y + y² 2x5 + 3xy' - dy dx O x¹y² + xy³ = 48 O x³y² + y³ = 120 о x²y² - y³ 3 = 56 O x³y² - xy³ =…

A:

Q: Find the area of the surface generated by revolving about the x-axis the ellipse x = acost, y =…

A:

Q: Evaluate the following limit, if it exists: lim x->7 = √x + 2 - 3 / x-7 (The square root covers…

A: In this question, we will evaluate the given limit expression.

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

A:

Q: Evaluate ¹ dx √√9-4x2 a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

A:

Q: Evaluate the following integrals S- 3 • │e* − e| + (e* + = e) + e) dx e 0

A:

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A: Given problem:- Suppose y = f(x) is a curve that always lies above the x-axis and never has a…

Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

A:

Q: Find the volume of the solid that results when the region enclosed by y = √√√x, y 0, and x = 49 is…

A:

Q: v (2uv²-3) du + (3u²v² - 3+4v)dv = 0 Ov(u²v² +3u + 2v) = c 2 Ov(u²v² +3u-2v) = c Ov(u²v²-3u-2v) = c…

A: We need to solve D.E.

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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

Q: Question 3: Show that 5xy² lim (x,y) (0,0) x² + y² does not exist.

A: Solve the following

Q: F/3 I ㅠ sec³ x tan x √2 + sec x dx

A:

Q: ¹In(1 + x) -dx X

A:

Q: Q3/ Use the definition of derivative to find f'(x) where fx=- 3 X+1

A:

Q: 2 cos xsinx V2+cosx 1. S- -dx

A: Given

Q: There are two 12-hour clocks, Clock A and Clock B. One clock is broken and it runs at a different…

A: Concept: There are two clocks A and B, one clock is broken and another one is normal which means…

Q: 64 Lood (vt. 1 √t + √i) dt

A: Given ∫164(t-1t+t3) dtTo evaluate the Integral:

Q: find the area the of region i) sketch the area, ii) Determine the boundaries ii) retup the definite…

A:

Q: The pedals of a bicycle are mounted on a bracket with centre 27.5 cm above ground. Each pedal is…

A: 1) Center = 27.5 cm  Radius = 17.5 cm  Rate = 10 cycles per minute => Rate (ω) = 1/6…

Q: 11 12 13 14 15 Solve Solve Solve Solve Solve ((AND)U(CNA))-(CNB) (BUC)-(DNA) (BUD)-(ANC) (ANB)U(DNC)…

A:

Q: (1 + y²)dx + (x²y + y + 2xy)dy = 0 Ox+2y² (1+x)² = c O 2x+y2(1+y)2= O 2x+y?(1+x)2=c y² x)² Ox+y²…

A: Solving by seperation of variables