*) dx Evaluate:

Q: Check the continuity of the function f(x). Explain why f(x) is continuous or not. x+1 =,x x2X > 1

A:

Q: 4.) f (x) = %3D x3 5.) f (x) = 2x² + Vx

A: we have to find the differentiation of given function

Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 Y 4 9 10 10 9 3 n 00

A:

Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

A:

Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 2 at x = 1. (Use…

A:

Q: Find the value of A which is defined as the angle between i+j and j+ k.

A:

Q: Question r Use the Second Derivative Test to find the location of all local extrema in the interval…

A:

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: Consider a function () whose dertvative ') continuous as shawn below Graph of f'(x), NOT f(x) 1 5 -1…

A:

Q: O Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2, y =

A:

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: I have stated the used formulas in the solution

Q: Q3) Evaluate triple integral y(x2 -y?)dz dx dy.

A:

Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 dx x2 + x – 2 y :

A:

Q: Find f'(1) if Aæ) = (x² –-x²-x+1)(x² + 1). 1 O 2 O -3

A:

Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2 y =

A:

Q: : / yº sech(e™mv) tanh (» ) dy 7lny Evaluate: @ -ch(7) + C None

A: Given problem:- ∫ y6 sech(e7ln(y)) tanh(e7ln(y)) dy

Q: Given that x=t3+t and y=3/2t4+t2, find dy/dx, d2y/dx2, d3y/dx3

A:

Q: Solve the D.E dy – (2x/1- y2)dx = 0

A:

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

A:

Q: Evaluate +V7dx 3 Oa.5 +C 2 5 3. Ob.2 3 2 Oc 2 sm +- Ot ast Od +C 3 2 52~

A: Evaluate integral

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

A:

Q: Determine a and b so that the function f(x) is continuous for all values of x. jika x <- 2 sin x…

A:

Q: g"(x) sin(x- 1) X-1 -4 13 h(x) = kr -8x+ 6, -1 10 4e-6-x+5, x>3 8 -1 (E) Find all x value(s) on the…

A: Given

Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0

A:

Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

A:

Q: Find f"(1) if fx) = x- 2x+ T. O 3n? - 2 O 31? – 1 12 - 21

A:

Q: The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A: Let r be the radius of spherical ballon

Q: Find the derivative of f(x)= (In x O a. 6x(In x) O b. 24(In xỷ c. 24 In x O d. 12(In x)

A:

Q: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x2 + 16

A: We have to solve above question

Q: Q2) Convert the polar functionr= tan20 to cartesian.

A:

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

A:

Q: QI) Evaluate the integral dx dy using polar coordinate

A: Solving

Q: Q2) Solve the D.E dy – (2x/1- y²)dx = 0

A:

Q: A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of…

A:

Q: Each of the following limits represents a derivative f'(a). (5 + h) - 125 (a) lim Choose the correct…

A:

Q: Verify that fy = fx ху ух f (x, y) = 2x'y' -x'y b. f(x,y)=(x' + y²)° а.

A:

Q: 22 – 9x? = 1 4.

A:

Q: Compute the length of the curve r(t)= (-3t, 3t + 7,–7t + 1) over the interval 0 <t <7

A:

Q: Evaluate: Je* cos (7e*)cos (4e*) dx ® -co (3*) -cos (11e') + C -(-*)* sin (3e“) –sin (11e*) +c A 22…

A: The given integral,       ∫excos7excos4exdx

Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: a. Neither I nor II

A:

Q: -6x-'dx

A:

Q: Differentiate D = x2 + sin25x with respect to t and simplify. x2 + sin? 5x dt dt x2 + sin2 5x)1/2 dt…

A:

Q: Find the general solution of (2x – y) dy = 2y – x - da

A:

Q: 3 5 8x 15 dx 5 x4 |

A:

Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

A:

Q: el-vidx

A:

Q: Evaluate the integral: (3si + 9s²j + 4k) ds

A:

Q: 2 3) -2

A: