Answers edited by Ananda Dasgupta

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What are the local extrema of $f (x) = x ln x - x e^{x}$ $f(x)= xlnx-xe^x$ ?
What is the integration of $\frac{d x}{x . \sqrt{x^{3} + 4}}$ $(dx)/(x.sqrt(x^3+4))$ ??
Integrate. What is the next step ?
Triangle A has an area of $15$ $15$ and two sides of lengths $4$ $4$ and $9$ $9$ . Triangle B is similar to triangle A and has a side of length $12$ $12$ . What are the maximum and minimum possible areas of triangle B?
A radioactive isotope $_{Z}^{X} A$ $""_Z^XA$ decay and emits one alpha particle and two beta particles consecutively. How to write the formula for the nuclides produced?
When a load is connected to a voltage divider, will the total resistance of the circuit increase or decrease?
Find the required limit algebrically, if it exists. lim (x+3)/(x-3) if x approaches 4 ?
$\int \sqrt{x^{2} + \frac{5}{x}} =$ $int sqrt(x^2+5/x)=$ ?
How to define a, b, c, d, e that are integer between 1-9 so that matrix is a symmetry matrix?
What is the solution to the integral of 2cosx + 3sinx / cosx + sinx? Thanks
A parellel plate capacitor with plate speration d is charged with a battery so that energy stored is $U$ $"U"$ . If a plate of dielectric $K$ $"K"$ and thickness d is placed betweeen the plates of capacitor and battery remains connected. The work by battery is?
What is the area of the shaded segment?
Find the sum of the infinite series $- \neq^{1 - n}$ $-ne^(1-n)$ from $n = 1$ $n=1$ to $\infty$ $oo$ ?
A circle touches two perpendicular lines $2 x - 3 y = 15$ $2x-3y=15$ and $3 x + 2 y = 3$ $3x+2y=3$ at the points $A (6, - 1)$ $A(6,-1)$ , $B (1, 0)$ $B(1,0)$ respectively. Find the equation of the circle?
Show that the line integral $\int_{- 1, 2}^{3, 1} (y^{2} + 2 x y) d x + (x^{2} + 2 x y) d y$ $int_{-1,2}^{3,1}(y^(2)+2xy)dx+(x^(2)+2xy)dy$ is independent of path and evaluate it?
How to derive 1st of motion from second law of motion?
How do you solve the inequality $x^{2} + 3 x - 28 < 0$ $x^2+3x-28<0$ ?
How do you solve for x given $∣ ∣ ∣ \frac{2 x}{7} + 9 ∣ ∣ ∣ > \frac{5}{7}$ $|\frac{2x}{7}+9 | > frac{5}{7}$ ?
If the AM and GM for 10 observations are both 15 then the value of harmonic mean......?
When $a - \frac{1}{a} = 1$ $a-1/a=1$ , $a^{5} - \frac{1}{a^{5}} =$ $a^5-1/a^5 =$ ? how to solve....
Find two numbers whose sum is 12 such that the sum of the square of one plus 4 times the other is a maximum?
An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?
What is the antiderivative of $ln (x^{2} + 2 x + 2)$ $ln(x^2 + 2x + 2)$ ?
How do you prove [(sinx-cosx)/(secx-cscx)]=[(sin2x)/2]?
$ψ_{A} (x, 0) = \sqrt{\frac{1}{6}} ϕ_{0} (x) + \sqrt{\frac{1}{3}} ϕ_{1} (x) + \sqrt{\frac{1}{2}} ϕ_{2} (x)$ $psi_A(x,0) = sqrt(1/6)phi_0(x) + sqrt(1/3)phi_1(x) + sqrt(1/2)phi_2(x)$ Calculate the expectation value $< E >$ $<E>$ at any later time t= $t_{1}$ $t_1$ , $ϕ_{n}$ $phi_n$ are energy eigenfunctions of the infinite potential well .Write the answer in terms of $E_{0}$ $E_0$ ?
How do you evaluate the integral $\int \sqrt{x} \sqrt{4 - x}$ $int sqrtxsqrt(4-x)$ ?
An object moves along a curve has an acceleration of 5 m/s^2 at 30° with its velocity of 5 m/s at some instant . The radius of curvature of the path at that instant is ? a) 10 m b) 20 m c) 5 m d)15 m
$y = f (x)$ $y=f(x)$ is given. Graph, $y = f (3 x) - 2$ $y=f(3x)-2$ and $y = - f (x - 1)$ $y=-f(x-1)$ ?
A particle begins to move with a tangential acceleration of constant magnitude $0.6 \frac{m}{s^{2}}$ $0.6m/s^2$ in a circular path. If it slips when it's total acceleration becomes $1 \frac{m}{s^{2}}$ $1m/s^2$ , then the angle through which it has turned before slipping is?
How to find result ?
F(x)=e^0.5x when x<=0 and f(x)=-(x-h)2+k when x>0 find h and k such that f(x) is both continuous and smooth at x=0?
Let $'f'$ be an even periodic function with period '4' such that $f(x) = 2^x-1$ , $0<=x<=2$ . The number of solutions of the equation $f(x) = 1$ in $[-10,20]$ are?
A frequency of variation of kinetic energy of a simple harmonic motion of frequency n is?
What is the derivative of $f(x)=sqrt(1+log_3(x)$ ?
What is the arclength of $(1/t^2,1/t)$ on $t in [1,2]$ ?
Integral Ln|x|/(1+x)^2 dx Answer Guys ???
I cut a triangle ABC out of a piece of paper. I found out that sinA+sinB+sinC=5/2 and a/sinA=16. What is the triangle’s perimeter?
Please solve with a detailed explanation?
In a garden a boy is swinging in the standing position how will the time period of the swing be affected if the boy sites down on the swing?
How do you factor the expression $-6 a^2 - ab + 7 b^2$ ?
$intint_Asqrt(xy-y^2)dxdyquadquadA={(x,y)inRR^2; 0<=y<=3, x/10<=y<=x}$ Would anyone help me?
A particle moves in the x-y plane with velocity $v_x$ = $8t-2$ and $v_y$ =2.If it passes through the points $x=14$ and $y$ =4 at $t$ =2,what is the equation of the path?
A circular loop wire with current I1=I∘π and a V shaped wire with current I2 are arranged in a plane as shown in diagram. If magnetic field at O is zero, value of I2 is ? (a) $(13aI_@)/35r$ (b) $(12aI_@)/17r$ (c) $(aI_@)/r$ (d) $(12aI_@)/35r$
A town's January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°?
Total resistance of the circuit ?
A particle of mass $m$ moving with speed $v$ hits elastically another stationary particle of mass $2m$ inside a smooth horizontal circular tube of radius $r$ . The time after which the second collision will happen?
Three rods each of mass M and length L, are joined together to form an equilateral triangle. What is the moment of inertia of a system about an Axis passing through its centre of mass and perpendicular to the plane of the triangle?
Integrate $x^3/sqrt((x^2+16))$ dx using trig substitution?
How do you solve $sin(x/2)-1=0$ between the interval $0<=x<8pi$ ?
What are the range of initial values using the Newton-Raphson method for $(x-9)/(x^2+1)=0$ for it to converge to 9?
How to complete this electrical current table?
How to integrate 1/(64x^2+100)?
A projectile is shot from the ground at an angle of $( pi)/3$ and a speed of $9 m/s$ . Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?
What is the answer please?
How many solutions are there to the following system of equations 4x – 8y = 0 and –3x + 8y = –7?
The number of solution of the equation 3^(sin2x+2cos2x)+ 3^(1-sin2x+2sin2x)=28 in [0,2π]?
Question #265f1
Find the Taylor series expansion formula of $f(x)=\lnx$ at $a=3$ ?
If the area under the curve of f(x) = 25 – x2 from x = –4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?
Find $i$ for $t>0$ if the circuit is in steady state at $t=0$ ?
The answer is?
17!/(5!*12!) ?