4. Evaluate the following limits: 5x2 – 33x + 40 (a) lim I-5 x2 – 14x + 45 Væ + 2 – 3 (b) lim x – 7

Q: 4. The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t3 – 15t² –...

A: Given- st=2t3-15t2-144t+7 To find- The time intervals in which object is slowing down or speeding up...

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx  

Q: Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant densit...

A:

Q: Use the given conditions to write an equation for the line in point-slope form and slope-intercept f...

A: Given that a line passes through point -3,-1 and 4,-1. We know that equation of line passes through ...

Q: Solve the inequality x2 + 3x - 10 > 0 using a graphing utility.

A: Given inequality is x2+3x-10>0.

Q: Q4(a) Apply Gauss-Jordan elimination method to solve the equations x – 2y + z = 0 2x + y – 3z = 5 4x...

A: Consider the given system of equations x-2y+z=02x+y-3z=54x-7y+z=-1 Write the system of equations in ...

Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3 ...

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: What does the Squeeze Theorem say?

A: In the calculus theorem are used to simplify the expression given or to simplify the complex mathema...

Q: Verify the identity:( tan θ cot θ) /csc θ= sin θ.

A: We have to verify the identity: tan θ cot θcosec θ=sin θ We know the formula of trigonometric functi...

Q: While integrating J Inx dx by integration by parts we get the value of v = а. 1 O b. Inx O c. 0 O d....

A: The given integral is ∫lnxdx. The rule for integration by parts is given by ∫udv=uv-∫vdu. We have to...

Q: Find an equation of a generating curve given the equation of its surface of revolution. 8x2 + y2 + z...

A: It is required to find the equation of generating curve given the equation of its surface of revolut...

Q: Find the binomial series for the functions (1 + x2)3

A: Find the binomial series for the functions (1 + x2)3

Q: If you know that -2 is a zero of f(x) = x3 + 7x2 + 4x - 12, explain how to solve the equation x3 + 7...

A: Given:                          fx=x3+7x2+4x-12 We know that -2 is a zero of fx=x3+7x2+4x-12        ...

Q: Write the answer in scientific notation (6.1 * 105)(4 * 10-9) ?

A:

Q: Integrate f(x, y, z) = x over the region in the first octant bounded above by z = 8 - 2x 2 - y2 and ...

A: Given that, z=8-2x2-y2        ...(1)z=y2              ...(2)

Q: Q3(a) Solve the following system of simultaneous linear equations using Gauss-Seidel method 5x, – x2...

A: The given system of equations is as follows. 5x1-x2=9-x1+5x2-x3=4-x2+5x3=-6 Rewrite the above equati...

Q: Use implicit differentiation to find dy/dx. xey − 10x + 3y = 0

A: The given equation is xey-10x+3y=0. Differentiate both sides of the above equation with respect to x...

Q: Determine whether f(x) approaches ∞ or −∞ as x approaches −2 from the left and from the right.

A: Given: --------------------------------------------------------------------------------------------...

Q: Find the derivative of the following function. y= -87x2 -9 dy 口 dx

A:

Q: How can the definition be used to verify limit statements for specific functions?

A: Let fx be the function of x. If for every positive number ∈ , however, small it may be , there exist...

Q: Factor completely : x2n + 6xn + 8

A: We have to factorize the expression: x2n+6xn+8 Factorization is the process of taking common from th...

Q: Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial functi...

A: Given: fx=-x3+x2+2x we know that as x→∞, fx→-∞ and as x→-∞,fx→∞ so, only graph of option c matches

Q: Explain the Chain Rule for two independent Variables ?

A: Chain rule for two independent variables: Let x=gu,v and y=hu,v be two differentaibel function of u ...

Q: Let f(y) -8+ In Determine the derivative f'(y) : ||

A: The function is given as, fy=-1-8+lny. The derivative of the function , f'y=-0-0-8+lny2=0. The funct...

Q: Let p(x) point (x, p(x)) when x = 4.7x14. Use a calculator or a graphing program to find the slope o...

A: The given function is  p(x) = 4.7*x1.4 To find the slope of the tangent we have to differentiate the...

Q: If f(x,y) = In(x?y² +3x) find- дудх O a. 12x?y (x²y² + 3x)? O b. 6x?y (x2у2 + 3x) Ob. 6x²y (x²y² + 3...

A:

Q: Find parametrizations for the line segments joining the points. Draw coordinate axes and sketch each...

A:

Q: Graph the polar equation r = 3cos θ. Be sure to test for symmetry.

A: we have to graph the polar equation r = 3cos θ.  We have to do test for symmetry.

Q: (c) Compute the inverse Fourier transform for the function Is| 4 F(6) = { -s, 0, * -s,

A:

Q: Write as a single logarithm: log(7x + 6) - log x.

A: The given expression is  log(7x + 6) - log x.   Log rule:   logca-logcb=logcab

Q: For what values of rFor what values of  y = e rx   satisfy the  equation   y " + 5 y ' - 6y=0

A: y''+5y'-6y=0 Let, y=erx⇒y'=r·erx⇒y''=r2·erx Therefore given differential equation becomes, y''+5y'-6...

Q: Suppose a class consists of 5 students majoring in Mathematics,5 students majoring in Islamic Studie...

A: The class consists of 5 students majoring in Mathematics,5 students majoring in Islamic Studies and ...

Q: For a certain endangered species, the goal is to have 1300 breeding adults in the wild by 2023. If p...

A:

Q: In the part where x> 0, whatever is in between goes forever, we're going to do integral calculati...

A: There is no area bounded by these two curves. but if we think at infinity they may be same. if we in...

Q: h(x) = [(x2 - 9) / (x - 3) if x ≠ 3 or 6 if x = 3]. Evaluate : a. h(5)           b. h(0)           c...

A: We have to evaluate the following: a. h5          b. h0        c. h3 Where function is hx=x2-9x-3 if...

Q: 2x - 4 Evaluate lim x+2 x2 - 4 x² – 4 O a. 0.75 O b. 0.25 O .1 O d. 0.5

A: Given: The given function is, limx→22x-4x2-4 The objective is to evaluate the given function using t...

Q: Use the properties of logarithms to expand the logarithmic expression. ln(3e2)

A: The given expression is ln3e2.  

Q: Areas of triangles Find the area of the following triangles T. The vertices of T are A(-1, -5, -3), ...

A:

Q: Fill in the blank/s : If two nonvertical lines are perpendicular, then theproduct of their slopes is...

A: we know that when two nonvertical lines are perpendicular, then the product of their slopes is -1

Q: A ball is thrown upward to a height of h0 meters. After each bounce, the ball rebounds to a fraction...

A: Given information: h0=30r=0.25  

Q: Evaluate the sums

A: The given series is: ∑k=16k2-5 Now expand the given series by substituting the values of k. ∑k=16k2-...

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.