Question a) b) 2xy Consider the function f(x, y) = 4x²+5y² Find the domain of f. Show that the limit does not exist. lim f(x,y) (x,y)-(0,0)

Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

A: Given data as follows :- Diameter of the semicircular gate is 4m. Height of the dam is 12 m.  Water…

Q: L 2x²³ + 8x doc 3 √x² + 4

A: This question can be solved using the concept of integration by substitution.

Q: Find the limit of the following sequence or determine that the sequence diverges. (-1)^) 4n+3

A: The given sequence,       -1n4n+3

Q: Differentiate and simplify this function:  e√t^2+t+1 - e-√t^2+t+1

A:

Q: if z=xarctan(y/z), find ∂z/∂x at x=0, y=1, z=1

A:

Q: Solve the following initial value problem: y(t) = = dy dt +0.9ty = 6t, y(0) = 1

A: Given: dydt+0.9ty=6t,      y0=1

Q: Find the curvature of the curve defined by the function y=3x^2 - 2x + 4 at the point x=2

A: Curvature is defined as : K(x) = |y"(x)| / {1 + [y'(x)]^2}^(3/2).  Note that :- |y"(x)| means the…

Q: Let the function f(x) have the property that f'(x) = ¹.1f g(x) = f(x²) find g'(x). g'(x) = Solution:

A:

Q: Complete the table by determining the amount of money P (present value) that should be invested at a…

A:

Q: if g(x, y) = yln(x) - x²ln(2y + 1) then 9x (2,0) = 0 Select one: O True O False

A:

Q: Let Find fy. f(x, y) = x²y + √√x + 5y

A:

Q: √(√3+)dx Select one: OA. OB. OC. OD. ³/2-² + 4x¹/2 + G ³/2² + 4x¹/2 + G ³/2² + 4x¹/2 - ³/2x² + с +…

A:

Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

A:

Q: The limit lim (x,y)→(-1,2) (x²y − 3xy²) = −8 - Select one: True False

A:

Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: Given the function f(x, y) = √2x + y = 1 - x + 1 Select one: O None of those O D= {(x, y)]y > 1 +…

A: To find out the domain of the given function..

Q: Evaluate: cot¹ (+) -do 0² O None of the choices Ocot³ (1)-cot (1) + 0 n ( ² ) − ² + c - ()επει ο -…

A:

Q: 10 20 30 (a) Draw the tangent line at each labeled point. y 5 4 3 2 1 O y st 5 4 3 2 1 10 20 30 10…

A: Please see the below picture for detailed solution.

Q: Find the arc length of the following curve on the given interval. x= 12t³, y=18t², 0sts √3 The arc…

A:

Q: Approximate the value of 22.5 O4 + 4 In(2) O4+2 In(2) O 6 O 4 +0.5 In(4)

A: The objective of the question is determine the approximate value of the given value.

Q: What is f(x) of f(x) = log3 (1-2x)²? -32 In(3)-(1-2x)³

A:

Q: Which of the following is a valid triple integral?

A: Which of the following is valid tripple integration

Q: Find 7 sin² (7x) dx

A:

Q: Solve the initial value problem: dy dz 9y, y(0) = 1

A:

Q: Calculate the volume of the solid bounded by the surfaces given by x2 + y2 = 1, z = 0 and z= x2 + y2

A:

Q: The graph below is a transformation of the absolute value function f(x) = |x|. Write the equation of…

A: We have to find the equation of transformed graph.

Q: ات, 01 +19+₂1 x+₂²0 +19+₂. 1. Evaluate

A:

Q: Integrate I -dz Select one: O A In 1-¹-2²+√1 − x² + C I OB. 21n1-¹³+√1 − x² + C | OC. In 1-²+√1 = z²…

A:

Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

A:

Q: Find the interest earned on $30,000 deposited into an account paying 2.5%. Round to the nearest…

A:

Q: Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of…

A: Sum of first n terms of a geometric sequence is given by Sn=arn-1r-1 where a is te first term and…

Q: Given: In (sin² 3t) = e = arc cot (w) Find: dw dt O(1+w²) (6cot (36) e) [ Oet+w²et - 6tan (3t) - 6w²…

A:

Q: Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 10…

A: topic- simple interest and equations

Q: given z=xlny-((2^x)/y)+ysinhsqrtx, find (∂^4)z/∂x∂y∂x∂y

A:

Q: f the measurement of the side of a cube is increased from 5 cm to 5.2 cm, the approximate increase…

A: Side of cube is increased from 5 to 5.2

Q: A polynomial f(x) and one or more of its zeros are given. f(x)=x²-8x³ +95x² +16x-194 4-9i is a zero…

A:

Q: Given the function f(x, y)= xye+tan² esec2 y The second derivative fyy of f is equal to 0. Select…

A:

Q: Calculate the integral where R is the region inside x ^2 + ?^ 2 = 4? and external to x ^2 + ? ^2 =…

A: We have to calculate the integral.

Q: A factory selling cell phones has a marginal cost function C(x) = 0.01² - 3x +229, where a…

A:

Q: √x +3 If f(x, y) = xy + 7 the domain of f(x, y). Select one: True False then the point (1, −7) is in

A:

Q: The differential equation Find such a solution and then give the related functions requested. dy =…

A:

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

A:

Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: The limit exists and is equal to 0. Select one: O True O False lim (x,y) →(0,0) 36x²+25y² 6x+5y

A:

Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find d ds for t = 1 and s = 2.

A:

Q: Evaluate S ○ In O Divergent ○ In 11 ○ 6 In 11 6 dr 2²-25 16

A: We need to evaluate integral.

Q: If f(x, y) = sin (xy) - yer, then f (0, 1) = -1. Select one: O True O False

A:

Q: -1 0 -t³+1 2 3+² e dt

A:

Q: 2 A force of F(x)=4cos (2x)-7 sin(x), x is in meters, acts on an object. What is the work required…

A:

Q: 1. Evaluate Sox2+4* dx 2. Find the area bounded by y = 4x², x = 2 and x = 6. 3. Find the area…

A: