tan(xy) = ? lim (х, у) >(,0) у+ 2ху 1 (c) 3 (а) 0 (b) (d) (е) 1

Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

A:

Q: Prove that lim (Snt tn)z ş + t Note: s = lim Sn ţ = llm

A:

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

A:

Q: Compute dy/dx using the limit definition of the first derivative for f(x) = 3x2

A: Given function is f(x)=3x2. we have to find the derivative using limit definition .

Q: lim at e -

A: Find the limit when x tends to 0

Q: If an object with mass m is dropped from rest, one model for its speed v after t seconds, taking air…

A: To find limit V , we will proceed as limit of function .V=mgc1-e-ctm

Q: Find the constant a such that Va ax +4-2 lim

A:

Q: [11 sec²(x) dx convergent divergent

A: We have to check that given integral is convergent or not.

Q: tan 3h 3. Estimate the value of lim,0- by creating a table of function values for h h = 0.01,0.001,…

A: We need to substitute these values of h in function f(h) to evaluate limit

Q: Find two paths of approach from which one can conclude that the function has no limit as (z, y)…

A: Given fx,y=x4-yx4+y

Q: Evaluate: 1- cos(x) lim 3x2 X+ 0 Express your answer in 4 decimal places.

A:

Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

A:

Q: 2. Show function f(x,y) = does not have limit of a function at point (0,0). 2² + ?

A: We need to show that the function does not have limit at point (0,0)

Q: TX-1 t. Lim ×つ○ 1

A: limx→0 πx-12x2    +πx(e2πx-1)=limx→0 πe2πxx-πx-e2πx+1+2πx2x2 (e2πx-1)   limx→0 πx-12x2…

Q: Show that limx,y)-(-2,0) g(x, y) does not exist given that (x + 2)³y² (x + 2)6 + 3y4' 0, if (x, y) +…

A:

Q: lim as x-->0  of (x+1-cosx)/x

A: The given limit of the function:

Q: How do you evaluate the limit:  limx-->0  (sin(4x))/9x WITHOUT using L'Hospital's Rule?

A: A property:L'Hospital's Rule is not necessary here.The following is an important property used in…

Q: Find the integral.

A: Given,

Q: Continuity equation is derived using the conservation

A: Equation of Continuity: The continuity equation states that in the case of steady…

Q: F ind @ Dlim Ix16/ lim 1-cos 3x 9. 4-X lim (1-secx) lim CosO 9= (9 -) 2.

A: Note :- there is an error in part (a) in this part value of limit is wrong. So i am solving…

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: aresin (2x-1) = 1-x 2 arctan

A: Substitute x = cos^2(theta) and simplify the equation.

Q: lim (In w-

A:

Q: 3x V1-x x = 0. y(x) = at Equation of the tangent line

A: Given,           yx=3x1-x2 at x=0

Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

A:

Q: hey you didnt state the assumptions of the model and the limintations as well

A: To state: Assumptions and limitations of an exponential model.

Q: compute limit as x goes to 0 of (sin(x)-x)/(x^3)

A:

Q: (i) Evaluate In (1-z³) lim 2->0 sin (2z

A: We need to evaluate the limit If the value of the function after putting the limit is in the…

Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

A:

Q: Express the limit as a definite integral on the given interval. lim 21 (x)2 + 7 Ax, [1, 8] dx

A:

Q: What

A: The correct option is (B).

Q: Show using sequences of functions that 2 lim e dx = 0.

A:

Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: Prove that lim vx sin (2) = 0 using the Squeeze Theorem. x-0+

A:

Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: 2 sin(Tr) Va – 1 Find lim

A: Explained below

Q: How do you evaluate the limit:  limx-->0 (1-cos(7t))/(sin(7t))   WITHOUT using L'Hospital's rule?

A: Since the given function is function of  variable t but in question limit is given for variable x.…

Q: Find the limit limx→0ln(1+4x)sin3x.

A:

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: 2xy Show that lim does not (x,y)→(0,0) x² + y² exist.

A: The limit function is limx,y→0,02xyx2+y2

Q: Compute limx→0 sin(x) − x / x^3

A: To find the limit, simplify the expression and then apply the limit to each term in the expression.…

Q: Find the equation of the tangent line of f(x)=2x^2-4x+1 at (2,1) using the limit definition of a…

A:

Q: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.