Divide the numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limit. Write ∞ or - o where appropriate. x -4 lim X00 9x +1

Q: 5/3 2. 2t4 tan 3x

A:

Q: Differentiate the function. f(x) = x³(x + 4) f'(x) =

A:

Q: z = x2 + y?, y = x²,y = 1, z = 0.

A:

Q: 3. j. lim f(x) k. lim f(x) X→3+ 3. 1. lim f (x) I m. lim f(x) x→3 y f(x) n. lim f(x) о. f (3) X→+∞

A:

Q: Find distance from point (-6, 3, 5) to the plane – 2y – 4z = 8| -

A:

Q: 2. Find the integral Jsec dx

A:

Q: A company selling widgets has found that the number of items sold, x, depends upon the price, p at w...

A:

Q: If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the following: In(a³b') (c) In(bc) - 3 1 а (d) (In ...

A:

Q: Solve the following initial value problem: (1+x²)y/ – 2xy = (1+x²)², y(1) = 6. %3D |

A: Given:     1+x2y'-2xy=1+x22             ,           y1=6

Q: group homomorphism preserves identity i.e. for any homomorphism, f :G → G' , if e is the identity el...

A: Proof be attached in second step hopefully you understand.

Q: Find the minimum and maximum values of the function y = 2613 + 39t² on [1,2] by comparing values at ...

A:

Q: A particle moves along a straight line with equation of motion s = f(t), where s is measured in mete...

A:

Q: Write the equation of the tangent line to the graph of y=x2  the point where x=2.5

A:

Q: 7. Consider the region above the r-axis and below y = e=² with x > 1, shown below. 1. Consider a wiz...

A:

Q: The graph of y = f(x) has the following features: f(– 2) = - 2 lim f(z) = 2 %3D H -2- lim f(r) = - 1...

A: Given : f(-2) = -2   

Q: For the following function, find the value of (a) f( – 3) and (b) f(4), if possible. x2 -1 if xs0 y ...

A:

Q: Verify that f has an inverse function. Then use the function f and the given real number a to find (...

A: f(x)=x+9x+3,  x>-3, a=2

Q: dw V4-9w2 2

A:

Q: Sove the differential equations (2y- 2x + X 1+ x²yz

A: Check given differential equation is exact or not. i.e.    My = Nx

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) g(t) = 6t...

A: Given query is to find the critical number of g(t).

Q: Give a value for c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the f...

A:

Q: 1. Find the resultant of the vectors A and B. A = 8a, + 7a, + 2a, В - - За, — 8а, - ба, Draw the vec...

A: Given that: A→=8ax+7ay+2azB→=-3ax-8ay-6az

Q: Use continuity to evaluate the following limit lim sin(x + cos(x)). Limit:

A: Given; Limx-π Sin(x+ cos(x)).

Q: Ordered: Baby formula 1:2 strength, 60 mL per hour to be diluted with SW. a. What is the equivalent ...

A:

Q: 4. S(1 – cos 4u) du 5. S sin x cos x dx

A: 4) Given:        ∫1-cos4udu Apply linearity:    =∫1 du-∫cos4u du     =u-∫cos4u du      

Q: What is the slope of the tangent line passing through y = x^2 - 3x - 5 at (-1, - 1)? Kindly show you...

A:

Q: Evaluate f(x – 1)Vxª – 4x – 2dæ -

A: Given:      ∫x3-1x4-4x-23dx      =∫x3-1x4-4x-213dx   substitute u=x4-4x-2          dudx=4x3-4→dx=14x...

Q: EVALUATE AND SOLVE THE LINEAR DE. (D5 – 15D3 + 10D² + 60D – 72)y = 0

A:

Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 3 and a root of multiplicity 1...

A: We know that a polynomial of degree n can be written in factors form as: P(x)=C x-x1·x-x2⋯⋯⋯x-xn Whe...

Q: Evaluate the following definite integral. |2x2 – 2x|dx

A: We have to find ∫-222x2-2xdx

Q: 3. [x*e"dx x'e

A: Given query is to find the value of the integral.

Q: 2. Find the volume of a cylinder with a radius of r and height h by integration.

A: Radius : r Hight : h

Q: sin 0 = 1 to determine the limit. Use the relation lim tan 0 lim 0→0 0 cot 7O

A: We know that  limθ→0 sin θθ = 1 Also  limθ→0 sinaθaθ = 1   where a is any real number.

Q: Let h(x) = sec(x). Find h'(0).

A:

Q: de +5x +6, dt / æ dt = 4t where: x(0) 2

A: It can be solved using laplace transform.

Q: 15) tan-l –1 --1 V2 17) cos 2 1 19) tan- 1

A: Given: 16)  tan-1-1

Q: -3 if x<-1 Н: у%33-1 H: y = if -1<x<3 4 if 2<x

A:

Q: X´- 2x - 63 Find the limits in a) through c) below for the function f(x)= Use – ∞ and o when appropr...

A: Given that: f(x)=x2-2x-63x-9

Q: Set f(x)= e=x². (a) What is the symmetry of the graph? (b) On what intervals does the function incre...

A: Given : f(x) = e-x²

Q: ds = f(t) (m/sec) of a body moving along a coordinate line. The accompanying figure shows the veloci...

A:

Q: 2x – 6 if x 4 Let f(æ) If f(x) is a function which is continuous everywhere, then we must have b :

A: Given query is to find the value of b.

Q: Given the closed region formed by the graphs y = 3x and y = x 2 in the first quadrant. If this regio...

A:

Q: Exercise 3.2.6 For the following matrices, determine if they are invertible. If so, use the formula ...

A:

Q: dt 七

A:

Q: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 13 1+x? (Use decimal notation...

A: NOTE: Refresh your page if you can't see any equations. . take x=3 the point on the curve is 

Q: or the function 2x – 4, 0 < x < 4 f(x) = { -2, x = 4 x2 – 8x + 20, 4< x se algebra to find each of t...

A: Given query is to find indicated limits.

Q: Solve the non-homogenous differential equation below dy 2y + x – 3 dx y+ 2х —3

A: Given that a non homogeneous differential equations and we solve by using general property of differ...

Q: QUESTION 5 lim f(x.y). Find (K)- (0,0) Let f(x.y)= O b.1 OC. -1 O d.1/2 e. Does not exist.

A:

Q: 1 ao et/2 dt = 0.50 2 An e-1/2 cos 2nt dt = 0.504 1+ 16n? 8n b, = et/2 sin 2nt dt = 0.504

A: a0 = (1/π) ∫0π e-t/2 dt , put -t/2 = x , dt = - 2dx Using formula ∫ et dt = et + c a0 = (1/π) ∫ ex (...

Q: Consider the function f(x) given by the graph below. y -5- f(x) -5 Determine the limits. If a limit ...

A: